Multi-Dose Pharmacokinetic Steady-State Peak (Cmax), Trough (Cmin) & Accumulation Calculator

Predict multi-dose drug accumulation factor R_ac = 1 / (1 − e^(−k·τ)).

Steady-State Peak Concentration (C_max,ss)
24.87 mg/L
Steady-State Trough (C_min,ss) 9.87 mg/L
Accumulation Ratio (R_ac) 1.66 ×
Peak-to-Trough Swing 15 mg/L
Inputs
mg/L
Initial concentration increment (C₀ = Dose / V_d) in mg/L.
hours
Dosing interval (τ) between administrations in hours.
hours
Drug elimination half-life (t₁/₂) in hours.
Results & Graph
Steady-State Peak Concentration (C_max,ss)
24.87 mg/L
Steady-State Trough (C_min,ss)
9.87 mg/L
Accumulation Ratio (R_ac)
1.66 ×
Peak-to-Trough Swing
15 mg/L

Steady-State Peak Concentration (C_max,ss)

Graph 1 • Single Dose Peak Mg L Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 mg/L 20.1 mg/L 40.3 mg/L 50%: 12.43 mg/L 12.4 50% 75%: 18.65 mg/L 18.6 75% 100%: 24.87 mg/L 24.9 100% 125%: 31.09 mg/L 31.1 125% 150%: 37.3 mg/L 37.3 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Steady-State Peak Concentration (C_max,ss) 24.87 mg/L Steady-State Trough (C_min,ss) 9.87 mg/L Accumulation Ratio (R_ac) 1.66 × Peak-to-Trough Swing 15 mg/L
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Steady-State Peak Concentration (C_max,ss)24.87 mg/LSteady-State Trough (C_min,ss)9.87 mg/LAccumulation Ratio (R_ac)1.66 ×Peak-to-Trough Swing15 mg/L
Summary: Dosing every 8 hrs with t₁/₂=6 hrs produces an accumulation factor of 1.66×, reaching steady-state C_max = 24.87 mg/L and trough C_min = 9.87 mg/L.
Summary: Dosing every 8 hrs with t₁/₂=6 hrs produces an accumulation factor of 1.66×, reaching steady-state C_max = 24.87 mg/L and trough C_min = 9.87 mg/L.
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Formula & Mathematical Methodology: Steady-State Peak & Trough Reference Equation

ke = ln(2) / t1/2
Rac = 1 / [ 1 − exp(−ke × τ) ]
Cmax,ss = C₀ × Rac
Cmin,ss = Cmax,ss × exp(−ke × τ)
k_e = ln(2) / t_1/2; R_ac = 1 / [ 1 − exp(−k_e × τ) ]; C_max,ss = C₀ × R_ac; C_min,ss = C_max,ss × exp(−k_e × τ)
  • singleDosePeakMgL: Single Dose Peak Mg L (mg/L)
  • dosingIntervalHours: Dosing Interval Hours (hours)
  • halfLifeHours: Half Life Hours (hours)

Rounding: Laboratory and clinical equations retain full floating-point precision and round displayed results to 2 decimal places.

Worked Example: Reference Calculation: Steady-State Peak & Trough

Predict multi-dose drug accumulation factor R_ac = 1 / (1 − e^(−k·τ)).

  1. Enter the reagent concentrations, assay readings, or clinical laboratory parameters.
  2. Compute the standard formula: k_e = ln(2) / t_1/2; R_ac = 1 / [ 1 − exp(−k_e × τ) ]; C_max,ss = C₀ × R_ac; C_min,ss = C_max,ss × exp(−k_e × τ).
  3. Review the primary result, supporting reference intervals, and 3 SVG visualizations.
Result: Evaluates Steady-State Peak & Trough via k_e = ln(2) / t_1/2; R_ac = 1 / [ 1 − exp(−k_e × τ) ]; C_max,ss = C₀ × R_ac; C_min,ss = C_max,ss × exp(−k_e × τ).

Frequently Asked Questions

What formula is used by the Multi-Dose Pharmacokinetic Steady-State Peak (Cmax), Trough (Cmin) & Accumulation Calculator?

It computes k_e = ln(2) / t_1/2; R_ac = 1 / [ 1 − exp(−k_e × τ) ]; C_max,ss = C₀ × R_ac; C_min,ss = C_max,ss × exp(−k_e × τ) and plots three custom SVG graphs showing parameter sensitivity and component breakdowns.

Can I compare different reagent dilutions or lab scenarios side by side?

Yes. Use the "Compare (0/3)" button to pin up to 3 scenarios side by side.

Are entered values stored on any server?

No. Every calculation runs 100% locally in your browser.

Health & Fitness · Pharmacology & Critical Care

Multi-Dose Pharmacokinetic Steady-State Peak (Cmax), Trough (Cmin) & Accumulation Calculator: inputs, method, and how to read the result

Predict multi-dose drug accumulation factor R_ac = 1 / (1 − e^(−k·τ)).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Single Dose Peak Mg L: Initial concentration increment (C₀ = Dose / V_d) in mg/L.
  • Dosing Interval Hours: Dosing interval (τ) between administrations in hours.
  • Half Life Hours: Drug elimination half-life (t₁/₂) in hours.

What the calculation includes

With the default values shown, Steady-State Peak Concentration (C_max,ss) is 24.87 mg/L. The calculation follows Steady-State Peak & Trough Reference Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Single Dose Peak Mg L from 15 mg/L to 16.5 mg/L changes Steady-State Peak Concentration (C_max,ss) from 24.87 mg/L to 27.36 mg/L. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard IUPAC atomic weights, 25°C (298.15 K) reference thermodynamics, and published clinical literature equations.
  • Educational and laboratory reference tool only; clinical scoring calculators do not replace professional medical judgment or institutional protocols.

Scope: IUPAC / NIH Laboratory & Clinical Reference Standard Check the assumptions and limitations against your situation before relying on the estimate.

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