What model does this calculator use?

It uses a one-compartment IV bolus model with first-order elimination.

What inputs are required?

Dose, volume of distribution, elimination half-life, and elapsed time are required. Decimal places are optional.

What units should I use?

Enter dose in mg, volume of distribution in L, and both half-life and time in hours. Concentration is reported in mg/L.

Can I use it for phenytoin or high-dose ethanol?

No. The model is not valid for Michaelis-Menten or other nonlinear pharmacokinetics, including phenytoin and high-dose ethanol.

Is this a dosing recommendation?

No. It is an educational calculation and is not medical advice. It also does not model multi-compartment distribution.

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Drug Half-Life Concentration Calculator

Estimate plasma drug concentration at a chosen time after an IV bolus using a one-compartment model with first-order elimination: C(t) = (Dose / Vd) · e^(-k·t), where k = ln2 / t½. Includes initial concentration C0, elimination rate constant k, percent remaining, and number of half-lives elapsed. Valid only for linear pharmacokinetics — NOT for Michaelis-Menten drugs (phenytoin, high-dose ethanol) or multi-compartment distribution. Reference: theophylline Vd ≈ 0.45 L/kg, t½ ≈ 8 h. Not medical advice.

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2 examples

Theophylline 400 mg IV after 8 h (one t½): C = 6.35 mg/L

C0 = 400/31.5 = 12.6984 mg/L; after t = t½, C = C0/2 = 6.3492 mg/L (50% remaining). Theophylline Vd ≈ 0.45 L/kg, t½ ≈ 8 h.

{"result":"C(8 h) = 6.3492 mg/L (50% of C0 remains). C0 = 12.6984 mg/L, k = 0.0866 h⁻¹.","metadata":{"input":{"dose":400,"vd":31.5,"halfLife":8,"time":8},"result":{"c0":12.6984,"ct":6.3492,"k":0.0866,"halfLivesElapsed":1,"percentRemaining":50,"percentEliminated":50,"model":"One-compartment, IV bolus, first-order elimination. Not medical advice."}}}

Drug after 2.5 half-lives: 17.68% remains

Dose=500 mg, Vd=50 L, t½=12 h, t=30 h (2.5 t½). C0=10 mg/L; C(30)=10·(1/2)^2.5=1.7678 mg/L (17.68% of C0).

{"result":"C(30 h) = 1.7678 mg/L (17.6777% of C0 remains). C0 = 10 mg/L, k = 0.0578 h⁻¹.","metadata":{"input":{"dose":500,"vd":50,"halfLife":12,"time":30},"result":{"c0":10,"ct":1.7678,"k":0.0578,"halfLivesElapsed":2.5,"percentRemaining":17.6777,"percentEliminated":82.3223,"model":"One-compartment, IV bolus, first-order elimination. Not medical advice."}}}

Inputs

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5 options

SettingsAdjust formats, ranges, numbers, and modes.5

Dose (mg)numberRequiredIV bolus dose. Must be positive.Volume of distribution Vd (L)numberRequiredApparent volume of distribution. Must be positive.Half-life t½ (h)numberRequiredElimination half-life in hours. Must be positive.Elapsed time t (h)numberRequiredTime elapsed since the IV bolus, in hours. Cannot be negative.Decimal PlacesnumberOptional

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Drug Half-Life Concentration Calculator

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Examples

1. Theophylline concentration after one half-life

2. Concentration after 2.5 half-lives

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