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Millimetre of mercury
Millimetre of mercury
Millimetre of mercury
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millimetre of mercury
Unit ofPressure
SymbolmmHg, mm Hg
Conversions
1 mmHg in ...... is equal to ...
   SI units   133.322 Pa
   English Engineering units   0.01933678 lbf/in2
Mercury barometer

A millimetre of mercury is a manometric unit of pressure, formerly defined as the extra pressure generated by a column of mercury one millimetre high. Currently, it is defined as exactly 133.322387415 pascals, or approximately[a] 1 torr = ⁠1/760⁠ atmosphere = ⁠101325/760⁠ pascals.[1][2] It is denoted mmHg[3] or mm Hg.[4][2]

Although not an SI unit, the millimetre of mercury is still often encountered in some fields; for example, it is still widely used in medicine, as demonstrated for example in the medical literature indexed in PubMed.[5] For example, the U.S. and European guidelines on hypertension, in using millimeters of mercury for blood pressure,[6] are reflecting the fact (common basic knowledge among health care professionals) that this is the usual unit of blood pressure in clinical medicine.

Definition

[edit]

The millimetre of mercury is defined as the pressure exerted by a column of mercury 1 millimetre high with a density of 13595.1 kg/m3 (approximate density at 0 °C or 32 °F) at standard gravity (9.80665 m/s2), i.e. precisely 133.322387415 pascals.

1 mmHg = 1 mm × 13595.1 kg/m3 × 9.80665 m/s2 = 133.322387415 Pa (exactly)

The use of an actual column of mercury for precise measurement of pressure requires corrections for the actual gravity at given location (±0.44%) and the density of mercury at the actual temperature (−0.45% at 25 °C or 77 °F). Precision may be further improved by taking account of the density of the fluid whose pressure is being measured.[7][clarification needed][verification needed]

A torr is a similar unit defined as exactly ⁠1/760⁠ of a standard atmosphere (1 atm = 101325 Pa), i.e. 133.322368421… pascals.

1 Torr = ⁠1/760⁠ atm = ⁠101325/760⁠ Pa = 133.322368421… Pa

The torr is about one part in seven million or 0.000015% smaller than the millimetre of mercury;[8] such difference is negligible for most practical uses.

Each millimetre of mercury can be divided into 1000 micrometres of mercury, denoted μmHg or simply microns.[9]

History

[edit]
Further information: Pressure head

For much of human history, the pressure of gases like air was ignored, denied, or taken for granted, but as early as the 6th century BC, Greek philosopher Anaximenes of Miletus claimed that all things are made of air that is simply changed by varying levels of pressure. He could observe water evaporating, changing to a gas, and felt that this applied even to solid matter. More condensed air made colder, heavier objects, and expanded air made lighter, hotter objects. This was akin to how gases become less dense when warmer and more dense when cooler.

In the 17th century, Evangelista Torricelli conducted experiments with mercury that allowed him to measure the presence of air. He would dip a glass tube, closed at one end, into a bowl of mercury and raise the closed end up out of it, keeping the open end submerged. The weight of the mercury would pull it down, leaving a partial vacuum at the far end. This validated his belief that air/gas has mass, creating pressure on things around it. Previously, the more popular conclusion, even for Galileo, was that air was weightless and it is vacuum that provided force, as in a siphon. The discovery helped bring Torricelli to the conclusion:

We live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight.

This test, known as Torricelli's experiment, was essentially the first documented pressure gauge.

Blaise Pascal went farther, having his brother-in-law try the experiment at different altitudes on a mountain, and finding indeed that the farther down in the ocean of atmosphere, the higher the pressure.

Mercury manometers were the first accurate pressure gauges. They are less used today due to mercury's toxicity, the mercury column's sensitivity to temperature and local gravity, and the greater convenience of other instrumentation. They displayed the pressure difference between two fluids as a vertical difference between the mercury levels in two connected reservoirs.

An actual mercury column reading may be converted to more fundamental units of pressure by multiplying the difference in height between two mercury levels by the density of mercury and the local gravitational acceleration. Because the specific weight of mercury depends on temperature and surface gravity, both of which vary with local conditions, specific standard values for these two parameters were adopted. This resulted in defining a "millimetre of mercury" as the pressure exerted at the base of a column of mercury 1 millimetre high with a precise density of 13595.1 kg/m3 when the acceleration due to gravity is exactly 9.80665 m/s2.

Use in medicine and physiology

[edit]

In medicine, pressure is still generally measured in millimetres of mercury. These measurements are in general given relative to the current atmospheric pressure: for example, a blood pressure of 120 mmHg, when the current atmospheric pressure is 760 mmHg, means 880 mmHg relative to perfect vacuum.

Routine pressure measurements in medicine include:

In physiology manometric units are used to measure Starling forces.

Pressure units
Pascal Bar Technical atmosphere Standard atmosphere Torr Pound per square inch
(Pa) (bar) (at) (atm) (Torr) (psi)
1 Pa — 10−5 bar 1.0197×10−5 at 9.8692×10−6 atm 7.5006×10−3 Torr 0.000145037737730 lbf/in2
1 bar 105 — = 1.0197 = 0.98692 = 750.06 = 14.503773773022
1 at 98066.5 0.980665 — 0.9678411053541 735.5592401 14.2233433071203
1 atm ≡ 101325 ≡ 1.01325 1.0332 — ≡ 760 14.6959487755142
1 Torr 133.322368421 0.001333224 0.00135951 ⁠1/760⁠ ≈ 0.001315789 — 0.019336775
1 psi 6894.757293168 0.068947573 0.070306958 0.068045964 51.714932572 —

See also

[edit]

Notes

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Millimetre of mercury

View on Grokipedia
from Grokipedia
The millimetre of mercury (mmHg), also known internationally as the torr (defined exactly as equal to 1 mmHg), is a non-SI unit of pressure defined as the pressure exerted at 0 °C by a 1-millimetre-high column of liquid mercury under standard gravitational acceleration of 9.80665 m/s². This unit originates from the measurement of mercury column height in barometers and is equivalent to exactly 133.322387415 Pa. Invented in 1643 by Italian physicist Evangelista Torricelli, the mercury barometer provided the first reliable method to quantify atmospheric pressure by observing the height of a mercury column in a vacuum tube inverted in a mercury reservoir, establishing the foundation for the mmHg unit. Torricelli's device demonstrated that air exerts pressure equivalent to about 760 mm of mercury at sea level, a standard later formalized as one atmosphere (1 atm = 760 mmHg). The torr was named in Torricelli's honor in the late 1940s, though mmHg remains the dominant notation in scientific and medical contexts. In modern applications, mmHg is widely used in to express , where normal arterial readings are less than 120 mmHg systolic and less than 80 mmHg diastolic (with typical values around 90–120/60–80 mmHg), measured via sphygmomanometers that historically relied on mercury columns but now often use aneroid or digital alternatives due to mercury's . It also persists in for barometric reporting and , despite international efforts to transition to SI units like pascals for standardization. The unit's persistence highlights its practical utility in fields requiring precise, intuitive scales tied to historical instrumentation.

Definition and Notation

Definition

The millimetre of mercury (mmHg) is a unit of defined as the exerted at the base of a column of mercury that is exactly 1 in height, measured under standard conditions of and . This unit originates from the principle of in manometers, where is balanced by the weight of the mercury column. The standard conditions for this definition specify a mercury density of 13.5951 g/cm³ at 0 °C and a gravitational acceleration of 9.80665 m/s², corresponding to the conventional value of standard gravity. The pressure PP is given by the hydrostatic formula P=ρgh,P = \rho g h, where ρ\rho is the density of mercury, gg is the gravitational acceleration, and hh is the height of the column (with h=0.001h = 0.001 m for 1 mm). Substituting the standard values yields P=(13.5951×103 kg/m3)×9.80665 m/s2×0.001 mP = (13.5951 \times 10^3 \, \mathrm{kg/m^3}) \times 9.80665 \, \mathrm{m/s^2} \times 0.001 \, \mathrm{m}. By international agreement, this pressure is exactly 133.322387415 pascals (Pa) in SI units, providing a precise link to the while retaining the unit's practical utility in manometric measurements.

Symbols and Equivalents

The primary symbol for the of mercury is mmHg, where "mm" represents and "Hg" is the for mercury, derived from the Latin term hydrargyrum. This notation omits any space between "mm" and "Hg" to ensure compactness in technical documentation. Alternative notations include , as well as the spaced variant mm Hg occasionally used in less formal contexts. Standards bodies provide guidelines for consistent usage of such non-SI units. The (ISO), in its ISO 80000-4 standard on quantities and units of mechanics, endorses notations like mmHg without periods, with lowercase for the element symbol and integration alongside SI units to maintain clarity in scientific and engineering applications; the National Institute of Standards and Technology (NIST) aligns with these conventions in its guides for unit representation.

Relation to SI Units

Conversion Factors

The millimetre of mercury (mmHg) converts to the pascal (Pa), the SI unit of pressure, as 1 mmHg = 133.322387415 Pa exactly, based on the standardized physical definition established in 1954 by the General Conference on Weights and Measures (CGPM). This value derives from the hydrostatic pressure formula P=ρghP = \rho g h, where h=1h = 1 mm = 0.001 m is the column height, ρ=13.5951×103\rho = 13.5951 \times 10^3 kg/m³ is the density of mercury at 0°C, and g=9.80665g = 9.80665 m/s² is the standard acceleration due to gravity. Substituting these yields P=(13.5951×103)×9.80665×0.001=133.322387415P = (13.5951 \times 10^3) \times 9.80665 \times 0.001 = 133.322387415 Pa. Common conversions to other units include 1 mmHg = 0.133322387415 kPa, 1 mmHg = 1.33322387415 mbar, and 1 mmHg ≈ 0.0193367748 psi. By convention, 1 atm = 760 mmHg exactly, so 1 mmHg = 1/760 atm ≈ 0.00131578947 atm. For precision in non-standard conditions, adjustments for temperature and local gravity are required, as they affect mercury density and the effective gravitational acceleration. Temperature variations alter density via ρ(T)=ρ0/[1+α(T−T0)]\rho(T) = \rho_0 / [1 + \alpha (T - T_0)], with α=1.818×10−4\alpha = 1.818 \times 10^{-4} °C⁻¹ (the volumetric thermal expansion coefficient), T0=0∘T_0 = 0^\circC, and ρ0=13595.1\rho_0 = 13595.1 kg/m³; thus, the adjusted pressure is P=[ρ(T)gh]P = [\rho(T) g h]. Local gravity glocalg_\text{local} replaces the standard gg in the formula, typically ranging from 9.780 to 9.832 m/s² depending on latitude and elevation. The following table provides key conversion factors for practical reference:
To UnitFactor (1 mmHg =)
Pa133.322387415
kPa0.133322387415
mbar1.33322387415
psi0.0193367748
atm1/760 (exact)
These factors assume standard conditions (0°C, standard g); corrections apply for deviations.

Equivalence to Torr

The millimetre of mercury (mmHg) and the are units of that have been defined as exactly equivalent since , with both equal to 101325760\frac{101325}{760} Pa, or approximately 133.322 Pa. This precise alignment ensures seamless interchangeability in calculations and measurements. The unit originated from a proposal by the on Vacuum Techniques of the , specifically to honor for his invention of the mercury in 1644. Prior to this formal naming, pressures were typically expressed in mmHg based on mercury column heights, but the provided a standardized, absolute reference tied to without direct dependence on physical mercury measurements. In practice, mmHg remains the preferred unit in medical and physiological applications, such as readings, due to its historical ties to manometric devices. Conversely, the is favored in vacuum physics, , and high-vacuum contexts for its convenience in expressing low pressures relative to atmosphere. The International Union of Pure and Applied Chemistry (IUPAC) formally adopted the in 1971 as a non-SI unit acceptable for use with the International System, recognizing its equivalence to mmHg and its entrenched role in legacy scientific practices despite the promotion of the pascal as the SI standard. This acceptance underscores the units' continued relevance while encouraging gradual transition to SI equivalents. Historically, the mmHg (and early conceptions of ) could vary slightly with local and mercury at 0 °C, introducing minor discrepancies on the order of parts per million. However, the modern definitions eliminate these variations, establishing an exact equivalence independent of environmental factors.

Historical Development

Invention by Torricelli

In 1643, , an Italian physicist and mathematician, invented the mercury barometer while serving as a secretary to . Influenced by Galileo's earlier experiments on , Torricelli sought to measure directly. He filled a , approximately four feet long and sealed at one end, completely with mercury and then inverted it into a dish containing mercury, allowing some liquid to flow out. This setup created a above the mercury column in the tube, with the height of the column stabilizing at about 760 millimeters at due to the balance between and the weight of the mercury. The theoretical foundation of Torricelli's invention rested on the idea that the atmosphere exerts a downward force capable of supporting a column of liquid, thereby disproving the Aristotelian notion of plenism—the belief that nature abhors a vacuum and that space is always filled with some substance. Instead, Torricelli's experiment demonstrated the existence of a true vacuum (later called Torricellian vacuum) above the mercury, where the column's height was determined solely by the pressure of the surrounding air pressing on the mercury in the dish. This breakthrough provided the first quantitative evidence of atmospheric pressure as a measurable physical phenomenon. Torricelli observed variations in the mercury column's height, noting that it decreased at higher altitudes, such as atop mountains, which he attributed to thinner air exerting less pressure. These early measurements established the height of the mercury column as a proxy for atmospheric pressure, laying the groundwork for pressure measurement in terms of liquid column heights, though the unit was initially expressed simply as millimeters or inches of mercury rather than the formalized "mmHg." His findings were described in a letter to Ricci dated 11 June 1644.

Standardization and Evolution

The adoption of the millimetre of mercury (mmHg) as a pressure unit gained momentum in the following Blaise Pascal's experiments in 1647, which confirmed Evangelista Torricelli's earlier observations on by demonstrating variations in mercury column height with altitude during the ascent. These results solidified the reliability of mercury barometers, leading to their widespread use across for meteorological and scientific measurements by the mid-1700s. In the , refinements focused on improving accuracy through standardization of mercury purity and reference conditions, with triple-distilled mercury becoming standard to eliminate impurities affecting density. The Committee of the British Association for the Advancement of developed the Meteorological Office standard around 1855, incorporating a 0°C reference for to account for of mercury and the scale. This design, detailed in a 1856 report, established a benchmark for consistent readings in national observatories and maritime applications. The 20th century brought international milestones in defining mmHg precisely. In 1954, the 10th Conférence Générale des Poids et Mesures (CGPM) established the exact equivalence of 1 mmHg to 133.322 pascals (Pa), based on mercury density at 0°C and of 9.80665 m/s² (corresponding to acceleration at 45° latitude). Parallel to these developments, the , named in honor of Torricelli, emerged as a related unit in the mid-20th century for use in vacuum technology, defined as exactly 1 mmHg. In 1971, the International Union of Pure and Applied Chemistry (IUPAC) formalized the equivalence of 1 to 1 mmHg within 2 × 10⁻⁷ relative uncertainty, facilitating interoperability in scientific applications. As of 2025, mmHg remains deprecated for new definitions in strict SI contexts under the 2019 revision, which fixed base units to constants without altering accepted non-SI units like mmHg. However, it is retained in per guidelines, which endorse dual reporting with kilopascals during transition but prioritize mmHg for blood pressure to avoid clinical errors. No substantive updates to its status have occurred since the 2019 revision.

Measurement Methods

Traditional Manometry

The U-tube manometer, a classical device for in millimetres of mercury (mmHg), consists of a U-shaped partially filled with mercury, where the two vertical arms allow for the observation of a difference in the columns caused by an applied differential. The tube typically features precision-bore tubing with a minimum of about 6.35 mm to minimize effects, and a scale positioned between the arms for direct reading of the mercury levels. In operation, an applied to one displaces the mercury, creating a height disparity Δh between the two menisci, which is directly proportional to the pressure difference via the hydrostatic P = ρ g Δh, where ρ is the of mercury, g is , and Δh is measured in mmHg. The reading is taken at the bottom of the concave meniscus in each , often using a cathetometer or for precision, with the expressed as the difference in mercury height at standard conditions. Traditional mercury manometers are classified into three main types based on their reference: absolute manometers measure pressure relative to a in one arm, gauge manometers compare against with one arm open to the air, and differential manometers assess the pressure difference between two external sources connected to each arm. These designs were essential for calibrating other instruments and providing primary standards in pressure measurement. Accuracy in readings requires corrections for several factors, including the meniscus shape due to , which typically necessitates an adjustment of approximately 0.3 mm for standard configurations. variations also affect precision, as mercury's changes by about 0.018% per °C deviation from 0°C, and the glass tube's must be accounted for to maintain reliable mmHg values. Proper scale alignment is critical to avoid errors from tilt or misalignment. Mercury U-tube manometers dominated pressure measurements in laboratories and medical settings until the mid-20th century, serving as the for against barometers due to their high accuracy, often achieving uncertainties as low as 0.01 mmHg. Their use persisted in scientific and industrial applications for reliable hydrostatic-based determinations until advancements in non-mercury alternatives emerged.

Modern Calibration Techniques

Modern calibration techniques for millimetre of mercury (mmHg) equivalents have shifted toward mercury-free methods to comply with environmental regulations and enhance precision in portable and digital devices. Aneroid barometers, which employ a mechanical diaphragm or capsule that deforms under , are calibrated directly to mmHg scales by comparing their readings to known atmospheric pressures obtained from reference sources, such as official weather services, and adjusting an internal screw for alignment. These devices are particularly suited for portable applications like field meteorology and basic sphygmomanometers, where their compact design allows for reliable mmHg-equivalent measurements without liquid columns. Electronic pressure transducers, including piezoelectric and strain-gauge types, convert mechanical into electrical signals that are processed to output digital values equivalent to mmHg, typically through standardized conversions like 1 mmHg ≈ 133.322 Pa. Calibration involves comparing the transducer's output against NIST-traceable primary standards, such as gauges or deadweight testers, which generate precise reference pressures up to several megapascals. These transducers achieve accuracies of ±0.1% in medical and industrial settings, enabling real-time digital displays calibrated to mmHg for applications requiring high . Calibration standards for mmHg-equivalent devices emphasize and to ensure reliability. NIST provides services using piston-gauge assemblies as primary standards, where effective areas are determined with uncertainties as low as 10 ppm, allowing secondary calibrations of transducers and manometers to mmHg scales. For medical devices, ISO 17025 protocols mandate biennial calibrations against certified references, often simulating mmHg ranges from 0 to 300 for blood pressure equipment, to maintain compliance and accuracy within ±3 mmHg. Deadweight testers serve as key tools in these processes, applying known gravitational forces to generate traceable pressures that align non-mercury instruments to historical mmHg definitions. Mercury-free alternatives have become standard in calibration setups, particularly for low-pressure ranges. Water or oil-filled U-tube manometers provide direct visual equivalents to mmHg by adjusting for fluid density and gravitational effects, offering resolutions down to 0.1 mmHg without toxic risks. In digital sphygmomanometers, software algorithms perform on-device conversions from sensor data to mmHg displays, calibrated periodically against aneroid or electronic references to ensure equivalence within clinical tolerances.

Applications

Medical and Physiological Uses

In clinical medicine, the millimetre of mercury (mmHg) serves as the primary unit for quantifying , recorded as systolic pressure over diastolic pressure using sphygmomanometers. This measurement assesses the force exerted by circulating blood on arterial walls, with normal adult values typically ranging from 90 to 120 mmHg systolic and 60 to 80 mmHg diastolic; readings below 90/60 mmHg indicate , while sustained elevations above 130/80 mmHg signal requiring intervention. The auscultatory technique, endorsed by the (AHA), employs a inflated to occlude brachial arterial flow—typically 20-30 mmHg above estimated systolic pressure—followed by gradual deflation while auscultating for over the . The onset of phase I sounds (tapping) marks systolic pressure, and the muffling or disappearance in phase V denotes diastolic pressure, providing a reliable noninvasive estimate aligned with invasive catheterization. AHA guidelines, updated through 2025, stress standardized positioning, multiple readings, and cuff size to minimize errors, with recent emphases on ambulatory monitoring for physiological variability. mmHg also features prominently in respiratory and neurological monitoring, such as (ICP), where normal supine values span 7 to 15 mmHg; elevations exceeding 20 mmHg can compress brain tissue, necessitating interventions like or osmotherapy. In , the unit gauges pressures, with normal mean values around 15 mmHg rising to 25-40 mmHg in conditions like , guiding ventilator adjustments to optimize oxygenation without . Gas partial pressures, including alveolar oxygen at approximately 100 mmHg, further contextualize ventilatory efficacy. Physiologically, mmHg captures arterial hydrostatic pressure—the gravitational and fluid dynamic force driving blood flow—which varies by posture, creating a vertical of about 40 mmHg from the heart to lower extremities in upright adults, influencing and autoregulation in organs like the and kidneys. Mercury-based sphygmomanometers, once ubiquitous for their precision, carry exposure risks from device breakage, releasing vapors that can cause acute , chronic neurological deficits, renal , and developmental harm in children via or skin contact. The , ratified in 2017, accelerated global phase-out of such devices by 2020 to curb environmental contamination and health hazards, promoting safer alternatives. Medical standardization favors mmHg for its historical accuracy and familiarity, as evidenced by the 2025 AHA/ACC guidelines, which set a treatment target of <130/80 mmHg for all adults with additional considerations for specific populations, preferring mmHg over SI units like pascals to ensure consistent clinical communication worldwide. This unit persists in automated oscillometric devices, which have largely replaced mercury models while preserving mmHg outputs for seamless integration into protocols.

Scientific and Industrial Uses

In vacuum technology, the millimetre of mercury (mmHg), equivalent to the , remains a prevalent unit for specifying partial pressures in analytical instruments such as and , where precise control of gas environments is essential. For instance, systems typically operate under high conditions around 10^{-7} mmHg to minimize and ensure accurate molecular fragmentation . Similarly, in applications like , partial pressures of gases are often measured in mmHg to quantify absorption lines and emission spectra without atmospheric interference. In , mmHg serves as a standard unit for barometric measurements, with the conventional sea-level value defined as 760 mmHg under conditions at 15°C. This benchmark facilitates altimetry calculations in and atmospheric modeling, where deviations from 760 mmHg indicate pressure gradients influencing patterns. Industrial applications leverage mmHg for in systems requiring or low-pressure environments, such as (HVAC) setups during refrigerant evacuation, where vacuums are targeted below 500 microns (0.5 mmHg) to remove and non-condensables. In , altimeters are calibrated to a standard setting of 29.92 inches of mercury, approximately equivalent to 760 mmHg, enabling consistent altitude readings above transition levels by compensating for local barometric variations. Within scientific laboratories, mmHg is routinely employed in gas law experiments, such as demonstrations of , where pressure-volume relationships for ideal gases are verified using manometers graduated in mmHg to track changes from atmospheric levels (760 mmHg) downward. sensor calibration in research settings also frequently references mmHg scales, particularly for validating transducers against mercury manometers in controlled experiments involving or ./10%3A_Gases/10.03%3A_The_Simple_Gas_Laws-_Boyles_Law_Charless_Law_and_Avogadros_Law) As of 2025, while the pascal (Pa) is increasingly adopted as the SI unit in modern vacuum research to align with international standards, mmHg persists in legacy equipment like microscopes, where operating vacuums are specified in (mmHg) for compatibility with older gauges and protocols in high-resolution imaging. This retention supports ongoing use in fields like , despite broader transitions to Pa for new instrumentation designs.

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