# Median lethal dose

In toxicology, the median lethal dose, LD$_{50}$ (abbreviation for "lethal dose, 50%"), LC$_{50}$ (lethal concentration, 50%) or LCt$_{50}$ is a toxic unit that measures the lethal dose of a given substance. The value of LD$_{50}$ for a substance is the dose required to kill half the members of a tested population after a specified test duration. LD$_{50}$ figures are frequently used as a general indicator of a substance's acute toxicity. A lower LD$_{50}$ is indicative of higher toxicity.
The term LD$_{50}$ 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. LD$_{50}$ is usually determined by tests on animals such as laboratory mice. In 2011, the U.S. Food and Drug Administration approved alternative methods to LD$_{50}$ for testing the cosmetic drug Botox without animal tests.

## Conventions

The LD$_{50}$ 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), 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 LC$_{50}$. 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 LD$_{50}$ is not the lethal dose for all subjects; some may be killed by much less, while others survive doses far higher than the LD$_{50}$. Measures such as "LD$_1$" and "LD$_{99}$" (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, LD$_{50}$ figures are often qualified with the mode of administration, e.g., "LD$_{50}$ i.v."
The related quantities LD$_{50}$/30 or LD$_{50}$/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 LCt$_{50}$, which relates to lethal dosage from exposure, where C is concentration and t is time. It is often expressed in terms of mg-min/m$^3$. ICt$_{50}$ 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/m$^3$ is equivalent to 10 minutes of 10 mg/m$^3$ (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 LC$_{50}$ 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.
For disease-causing organisms, there is also a measure known as the median infective dose and dosage. The median infective dose (ID$_{50}$) is the number of organisms received by a person or test animal qualified by the route of administration (e.g., 1,200 org/man per oral). Because of the difficulties in counting actual organisms in a dose, infective doses may be expressed in terms of biological assay, such as the number of LD$_{50}$s to some test animal. In biological warfare infective dosage is the number of infective doses per cubic metre of air times the number of minutes of exposure (e.g., ICt$_{50}$ is 100 medium doses - min/m$^3$).

## Limitation

As a measure of toxicity, LD$_{50}$ is somewhat unreliable and results may vary greatly between testing facilities due to factors such as the genetic characteristics of the sample population, animal species tested, environmental factors and mode of administration.
There can be wide variability between species as well; what is relatively safe for rats may very well be extremely toxic for humans (cf. paracetamol toxicity), and vice versa. For example, chocolate, comparatively harmless to humans, is known to be toxic to many animals. When used to test venom from venomous creatures, such as snakes, LD$_{50}$ results may be misleading due to the physiological differences between mice, rats, and humans. Many venomous snakes are specialized predators on mice, and their venom may be adapted specifically to incapacitate mice; and mongooses may be exceptionally resistant. While most mammals have a very similar physiology, LD$_{50}$ results may or may not have equal bearing upon every mammal species, such as humans, etc.

## Examples

Note: Comparing substances (especially drugs) to each other by LD$_{50}$ can be misleading in many cases due (in part) to differences in effective dose (ED$_{50}$). Therefore, it is more useful to compare such substances by therapeutic index, which is simply the ratio of LD$_{50}$ to ED$_{50}$.
The following examples are listed in reference to LD$_{50}$ values, in descending order, and accompanied by LC$_{50}$ values, {bracketed}, when appropriate.
| Substance | Animal, route | LD$_{50}$ {LC$_{50}$} | LD$_{50}$ : g/kg {LC$_{50}$ : g/L} standardised |
| Water (H$_2$O) | rat, oral | >90,000 mg/kg | >90 |
| Sucrose (table sugar) | rat, oral | 29,700 mg/kg | 29.7 |
| Corn syrup | rat, oral | 25,800 mg/kg | 25.8 |
| Glucose (blood sugar) | rat, oral | 25,800 mg/kg | 25.8 |
| Monosodium glutamate (MSG) | rat, oral | 16,600 mg/kg | 16.6 |
| Stevioside (from stevia) | mice and rats, oral | 15,000 mg/kg | 15 |
| Gasoline (petrol) | rat | 14,063 mg/kg | 14.0 |
| Vitamin C (ascorbic acid) | rat, oral | 11,900 mg/kg | 11.9 |
| Glyphosate (isopropylamine salt of) | rat, oral | 10,537 mg/kg | 10.537 |
| Lactose (milk sugar) | rat, oral | 10,000 mg/kg | 10 |
| Aspartame | mice, oral | 10,000 mg/kg | 10 |
| Urea (OC(NH$_2$)$_2$) | rat, oral | 8,471 mg/kg | 8.471 |
| Cyanuric acid | rat, oral | 7,700 mg/kg | 7.7 |
| Cadmium sulfide (CdS) | rat, oral | 7,080 mg/kg | 7.08 |
| Ethanol (CH$_3$CH$_2$OH) | rat, oral | 7,060 mg/kg | 7.06 |
| Sodium isopropyl methylphosphonic acid (IMPA, metabolite of sarin) | rat, oral | 6,860 mg/kg | 6.86 |
| Melamine | rat, oral | 6,000 mg/kg | 6 |
| Taurine | rat, oral | 5,000 mg/kg | 5 |
| Melamine cyanurate | rat, oral | 4,100 mg/kg | 4.1 |
| Fructose (fruit sugar) | rat, oral | 4,000 mg/kg | 4 |
| Sodium molybdate (Na$_2$MoO$_4$) | rat, oral | 4,000 mg/kg | 4 |
| Sodium chloride (table salt) | rat, oral | 3,000 mg/kg | 3 |
| Aspirin (acetylsalicylic acid) | rat, oral | 1,944 mg/kg | 1.944 |
| Delta-9-tetrahydrocannabinol (THC) | rat, oral | 1,270 mg/kg | 1.27 |
| Cannabidiol (CBD) | rat, oral | 980 mg/kg | 0.98 |
| Methanol (CH$_3$OH) | human, oral | 810 mg/kg | 0.81 |
| Trinitrotoluene (TNT) | rat, oral | 790 mg/kg | 0.790 |
| Arsenic (As) | rat, oral | 763 mg/kg | 0.763 |
| Ibuprofen | rat, oral | 636 mg/kg | 0.636 |
| Formaldehyde (CH$_2$O) | rat, oral | 600–800 mg/kg | 0.6 |
| Solanine (main alkaloid in the several plants in Solanaceae amongst them Solanum tuberosum) | rat, oral (2.8 mg/kg human, oral) | 590 mg/kg | 0.590 |
| Alkyl dimethyl benzalkonium chloride (ADBAC) | rat, oral fish, immersion aquatic invertebrates, immersion | 304.5 mg/kg {0.28 mg/L} {0.059 mg/L} | 0.3045 {0.00028} {0.000059} |
| Coumarin (benzopyrone, from Cinnamomum aromaticum and other plants) | rat, oral | 293 mg/kg | 0.293 |
| Psilocybin (from magic mushrooms) | mouse, oral | 280 mg/kg | 0.280 |
| Hydrochloric acid (HCl) | rat, oral | 238–277 mg/kg | 0.238 |
| Ketamine | rat, intraperitoneal | 229 mg/kg | 0.229 |
| Paracetamol (acetaminophen) | rat, oral | 200 mg/kg | 0.2 |
| Caffeine | rat, oral | 192 mg/kg | 0.192 |
| Arsenic trisulfide (As$_2$S$_3$) | rat, oral | 185–6,400 mg/kg | 0.185–6.4 |
| Sodium nitrite (NaNO$_2$) | rat, oral | 180 mg/kg | 0.18 |
| Methylenedioxymethamphetamine (MDMA, ecstasy) | rat, oral | 160 mg/kg | 0.18 |
| Uranyl acetate dihydrate (UO$_2$(CH$_3$COO)$_2$) | mouse, oral | 136 mg/kg | 0.136 |
| Dichlorodiphenyltrichloroethane (DDT) | mouse, oral | 135 mg/kg | 0.135 |
| Uranium (U) | mice, oral | 114 mg/kg (estimated) | 0.114 |
| Bisoprolol | mouse, oral | 100 mg/kg | 0.1 |
| Cocaine | mouse, oral | 96 mg/kg | 0.096 |
| Cobalt(II) chloride (CoCl$_2$) | rat, oral | 80 mg/kg | 0.08 |
| Cadmium oxide (CdO) | rat, oral | 72 mg/kg | 0.072 |
| Thiopental sodium (used in lethal injection) | rat, oral | 64 mg/kg | 0.064 |
| Demeton-S-methyl | rat, oral | 60 mg/kg | 0.060 |
| Methamphetamine | rat, intraperitoneal | 57 mg/kg | 0.057 |
| Sodium fluoride (NaF) | rat, oral | 52 mg/kg | 0.052 |
| Nicotine | mouse and rat, oral human, smoking | 50 mg/kg | 0.05 |
| Pentaborane | human, oral | 50 mg/kg | 0.05 |
| Capsaicin | mouse, oral | 47.2 mg/kg | 0.0472 |
| Vitamin D3 (cholecalciferol) | rat, oral | 37 mg/kg | 0.037 |
| Piperidine (from black pepper) | rat, oral | 30 mg/kg | 0.030 |
| Heroin (diamorphine) | mouse, intravenous | 21.8 mg/kg | 0.0218 |
| Lysergic acid diethylamide (LSD) | rat, intravenous | 16.5 mg/kg | 0.0165 |
| Arsenic trioxide (As$_2$O$_3$) | rat, oral | 14 mg/kg | 0.014 |
| Metallic arsenic (As) | rat, intraperitoneal | 13 mg/kg | 0.013 |
| Sodium cyanide (NaCN) | rat, oral | 6.4 mg/kg | 0.0064 |
| Chlorotoxin (CTX, from scorpions) | mice | 4.3 mg/kg | 0.0043 |
| Hydrogen cyanide (HCN) | mouse, oral | 3.7 mg/kg | 0.0037 |
| Carfentanil | rat, intravenous | 3.39 mg/kg | 0.00339 |
| Nicotine (from various Solanaceae genera) | mice, oral | 3.3 mg/kg | 0.0033 |
| White phosphorus (P) | rat, oral | 3.03 mg/kg | 0.00303 |
| Strychnine (from Strychnos nux-vomica) | human, oral | 1–2 mg/kg (estimated) | 0.001–0.002 |
| Aconitine (from Aconitum napellus and related species) | human, oral | 1–2 mg/kg | 0.001–0.002 |
| Mercury(II) chloride (HgCl$_2$) | rat, oral | 1 mg/kg | 0.001 |
| Cantharidin (from blister beetles) | human, oral | 500 μg/kg | 0.0005 |
| Aflatoxin B1 (from Aspergillus flavus mold) | rat, oral | 480 μg/kg | 0.00048 |
| Plutonium (Pu) | dog, intravenous | 320 μg/kg | 0.00032 |
| Bufotoxin (from Bufo toads) | cat, intravenous | 300 μg/kg | 0.0003 |
| Brodifacoum | rat, oral | 270 μg/kg | 0.00027 |
| Caesium-137 ($^{137}$ Cs) | mouse, parenteral | 21.5 μCi/g | 0.000245 |
| Sodium fluoroacetate (CH$_2$FCOONa) | rat, oral | 220 μg/kg | 0.00022 |
| Chlorine trifluoride (ClF$_3$) | mouse, absorption through skin | 178 μg/kg | 0.000178 |
| Sarin | mouse, subcutaneous injection | 172 μg/kg | 0.000172 |
| Robustoxin (from Sydney funnel-web spider) | mice | 150 μg/kg | 0.000150 |
| VX | human, oral, inhalation, absorption through skin/eyes | 140 μg/kg (estimated) | 0.00014 |
| Venom of the Brazilian wandering spider | rat, subcutaneous | 134 μg/kg | 0.000134 |
| Amatoxin (from Amanita phalloides mushrooms) | human, oral | 100 μg/kg | 0.0001 |
| Dimethylmercury (Hg(CH$_3$)$_2$) | human, transdermal | 50 μg/kg | 0.000050 |
| TBPO (t-Butyl-bicyclophosphate) | mouse, intravenous | 36 μg/kg | 0.000036 |
| Fentanyl | monkey | 30 μg/kg | 0.00003 |
| Venom of the Inland Taipan (Australian snake) | rat, subcutaneous | 25 μg/kg | 0.000025 |
| Ricin (from castor oil plant) | rat, intraperitoneal rat, oral | 22 μg/kg 20–30 mg/kg | 0.000022 0.02 |
| 2,3,7,8-Tetrachlorodibenzodioxin (TCDD, in Agent Orange) | rat, oral | 20 μg/kg | 0.00002 |
| Tetrodotoxin from the blue-ringed octopus | intravenous | 8.2 μg/kg | 0.0000082 |
| CrTX-A (from Carybdea rastonii box jellyfish venom) | crayfish, intraperitoneal | 5 μg/kg | 0.000005 |
| Latrotoxin (from widow spider venom) | mice | 4.3 μg/kg | 0.0000043 |
| Epibatidine (from Epipedobates anthonyi poison dart frog) | mouse, intravenous | 1.46-13.98 μg/kg | 0.00000146 |
| Batrachotoxin (from poison dart frog) | human, sub-cutaneous injection | 2–7 μg/kg (estimated) | 0.000002 |
| Abrin (from rosary pea) | mice, intravenously human, inhalation human, oral | 0.7 μg/kg 3.3 μg/kg 10–1000 μg/kg | 0.0000007 0.0000033 0.00001–0.001 |
| Saxitoxin (from certain marine dinoflagellates) | human, intravenously human, oral | 0.6 μg/kg 5.7 μg/kg | 0.0000006 0.0000057 |
| Pacific Ciguatoxin-1 (from ciguateric fish) | mice, intraperitoneal | 250 ng/kg | 0.00000025 |
| Palytoxin (from Palythoa coral) | mouse, intravenous | 45 ng/kg 2.3–31.5 μg/kg | 0.000000045 0.0000023 |
| Maitotoxin (from ciguateric fish) | mouse, intraperitoneal | 50 ng/kg | 0.00000005 |
| Polonium-210 ($^{210}$ Po) | human, inhalation | 10 ng/kg (estimated) | 0.00000001 |
| Diphtheria toxin (from Corynebacterium) | mice | 10 ng/kg | 0.00000001 |
| Shiga toxin (from Shigella bacteria) | mice | 2 ng/kg | 0.000000002 |
| Tetanospasmin (from Clostridium tetani) | mice | 2 ng/kg | 0.000000002 |
| Botulinum toxin (from Clostridium botulinum) | human, oral, injection, inhalation | 1 ng/kg (estimated) | 0.000000001 |
| Ionizing radiation | human, irradiation | 3–5 Gy (Gray) | — |

## Poison scale

The LD$_{50}$ values have a very wide range. The botulinum toxin as the most toxic substance known has an LD$_{50}$ value of 1 ng/kg, while the most non-toxic substance water has an LD$_{50}$ value of more than 90 g/kg; a difference of about 1 in 100 billion, or 11 orders of magnitude. As with all measured values that differ by many orders of magnitude, a logarithmic view is advisable. Well-known examples are the indication of the earthquake strength using the Richter scale, the pH value, as a measure for the acidic or basic character of an aqueous solution or of loudness in decibels. In this case, the negative decimal logarithm of the LD$_{50}$ values, which is standardized in kg per kg body weight, is considered −log$_{10}$(LD$_{50}$).
The dimensionless value found can be entered in a toxin scale. Water as the baseline substance is nearly 1 in the negative logarithmic toxin scale.

## Procedures

A number of procedures have been defined to derive the LD$_{50}$. The earliest was the 1927 "conventional" procedure by Trevan, which requires 40 or more animals. The fixed-dose procedure, proposed in 1984, estimates a level of toxicity by feeding at defined doses and looking for signs of toxicity (without requiring death). The up-and-down procedure, proposed in 1985, yields an LD$_{50}$ value while dosing only one animal at a time.