Median lethal dose

In toxicology, the median lethal dose, LD₅₀ (abbreviation for "lethal dose, 50%"), LC₅₀ (lethal concentration, 50%) or LCt₅₀ is a toxic unit that measures the lethal dose of a given substance. The value of LD₅₀ for a substance is the dose required to kill half the members of a tested population after a specified test duration. LD₅₀ figures are frequently used as a general indicator of a substance's acute toxicity. A lower LD₅₀ is indicative of higher toxicity.

The term LD₅₀ is generally attributed to John William Trevan. The test was created by J. W. Trevan in 1927. The term semilethal dose is occasionally used in the same sense, in particular with translations of foreign language text, but can also refer to a sublethal dose. LD₅₀ is usually determined by tests on animals such as laboratory mice. In 2011, the U.S. Food and Drug Administration approved alternative methods to LD₅₀ for testing the cosmetic drug botox without animal tests.

The LD₅₀ is usually expressed as the mass of substance administered per unit mass of test subject, typically as milligrams of substance per kilogram of body mass, sometimes also stated as nanograms (suitable for botulinum toxin), micrograms, or grams (suitable for paracetamol) per kilogram. Stating it this way allows the relative toxicity of different substances to be compared and normalizes for the variation in the size of the animals exposed (although toxicity does not always scale simply with body mass). For substances in the environment, such as poisonous vapors or substances in water that are toxic to fish, the concentration in the environment (per cubic metre or per litre) is used, giving a value of LC₅₀. But in this case, the exposure time is important (see below).

The choice of 50% lethality as a benchmark avoids the potential for ambiguity of making measurements in the extremes and reduces the amount of testing required. However, this also means that LD₅₀ is not the lethal dose for all subjects; some may be killed by much less, while others survive doses far higher than the LD₅₀. Measures such as "LD₁" and "LD₉₉" (dosage required to kill 1% or 99%, respectively, of the test population) are occasionally used for specific purposes.

Lethal dosage often varies depending on the method of administration; for instance, many substances are less toxic when administered orally than when intravenously administered. For this reason, LD₅₀ figures are often qualified with the mode of administration, e.g., "LD₅₀ i.v."

The related quantities LD₅₀/30 or LD₅₀/60 are used to refer to a dose that without treatment will be lethal to 50% of the population within (respectively) 30 or 60 days. These measures are used more commonly within radiation health physics, for ionizing radiation, as survival beyond 60 days usually results in recovery.

A comparable measurement is LCt₅₀, which relates to lethal dosage from exposure, where C is concentration and t is time. It is often expressed in terms of mg-min/m³. ICt₅₀ is the dose that will cause incapacitation rather than death. These measures are commonly used to indicate the comparative efficacy of chemical warfare agents, and dosages are typically qualified by rates of breathing (e.g., resting = 10 L/min) for inhalation, or degree of clothing for skin penetration. The concept of Ct was first proposed by Fritz Haber and is sometimes referred to as Haber's law, which assumes that exposure to 1 minute of 100 mg/m³ is equivalent to 10 minutes of 10 mg/m³ (1 × 100 = 100, as does 10 × 10 = 100).

Some chemicals, such as hydrogen cyanide, are rapidly detoxified by the human body, and do not follow Haber's law. In these cases, the lethal concentration may be given simply as LC₅₀ and qualified by a duration of exposure (e.g., 10 minutes). The material safety data sheets for toxic substances frequently use this form of the term even if the substance does follow Haber's law.