Therapeutic Index Calculator
The therapeutic index (TI) is a fundamental pharmacology concept that quantifies the margin between a drug's therapeutic and toxic doses. Calculated as TI = TD50 / ED50, a TI greater than 1 indicates the toxic dose exceeds the effective dose, while a TI close to 1 signals a narrow therapeutic window. Drugs with narrow TI values (lithium, digoxin, warfarin, aminoglycosides, antiepileptics) require blood level monitoring and individualized dosing. High-TI drugs (most over-the-counter medications) have wide safety margins and are less prone to accidental toxicity.
Therapeutic index formula
TI = TD50 / ED50
TD50 = median toxic dose; ED50 = median effective dose. Both are in the same units (typically mg/kg in animal studies). TI below 2 is generally considered narrow; TI above 10 is considered wide. Some references use LD50 in place of TD50 for preclinical assessment.
Examples of narrow vs wide therapeutic index drugs
- Narrow TI (close monitoring required): digoxin, lithium, warfarin, gentamicin, vancomycin, phenytoin, carbamazepine, theophylline.
- Intermediate TI: many antibiotics, antihypertensives, and antidiabetic agents.
- Wide TI (generally safer): acetaminophen (though toxic in overdose), most antihistamines, NSAIDs at normal doses.
- The FDA defines a narrow therapeutic index drug as one where small dose changes lead to significant changes in pharmacodynamic response or toxicity.
Therapeutic index calculator: frequently asked questions
What is the therapeutic index?
The therapeutic index (TI) is the ratio of the toxic dose to the effective dose for a drug: TI = TD50 / ED50. It measures the safety margin between the dose that produces toxicity in 50% of subjects (TD50) and the dose that produces the desired therapeutic effect in 50% of subjects (ED50).
What is a narrow therapeutic index drug?
Drugs with a TI close to 1 have a narrow therapeutic window, meaning the toxic dose is close to the effective dose. Examples include digoxin, warfarin, lithium, phenytoin, and aminoglycosides. These drugs require careful monitoring and precise dosing.
What is TD50?
TD50 (median toxic dose) is the dose that produces a toxic effect in 50% of a test population. In animals, a related concept is LD50 (lethal dose in 50%), which may be used when calculating TI in preclinical safety studies.
What is ED50?
ED50 (median effective dose) is the dose that produces the desired therapeutic effect in 50% of a population. It is derived from dose-response curves in pharmacological studies.
Can this calculator be used for clinical patient care?
No. TI is a population-level pharmacological parameter used in drug development and safety assessment, not a patient-specific clinical dosing tool. Clinical dosing should use established therapeutic ranges, blood level monitoring, and professional judgment.
Official sources
- U.S. Food and Drug Administration: FDA Orange Book Preface (narrow TI drugs).
- NIH National Library of Medicine: Pharmacokinetics (StatPearls).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.