Model methodology

What the curve means—and exactly how it is drawn.

Model scopeSubcutaneous injection schedules

Population-average concentration estimate—not an individual prediction or measured blood level.

01 · Model 02 · Parameters 03 · Validation 04 · Limits 05 · Sources

The model

One dose, then every dose.

Semaglutide and tirzepatide default to a simpler one-compartment estimate and offer an optional two-compartment population model based on richly sampled clinical pharmacology data. Retatrutide has only the fitted one-compartment surrogate because a parameter-complete two-compartment population model is not available for this calculator.

One-compartment option — one injection

P_{i} = \frac{D_{i} \cdot 1000}{V / F} \cdot \frac{k_{a}}{k_{a} - k_{e}}

E_{r} (Δt) = e^{- rΔt}

C_{i} (t) = P_{i} [E_{k_{e}} (Δt) - E_{k_{a}} (Δt)]

Δt = t - t_{i}; C_{i} = 0 when Δt < 0

This Bateman function is the default for semaglutide and tirzepatide and the only available structure for retatrutide. For Δt = t − tᵢ < 0, Cᵢ(t) = 0.

Semaglutide and tirzepatide — two-compartment macro rates

k_{10} = \frac{CL}{V_{c}}

k_{12} = \frac{Q}{V_{c}}

k_{21} = \frac{Q}{V_{p}}

S = k_{10} + k_{12} + k_{21}

α, β = \frac{S \pm \sqrt{S^{2} - 4 k_{10} k_{21}}}{2}

The central and peripheral compartments exchange drug through Q; elimination occurs from the central compartment through CL.

Two-compartment central plasma concentration

g (r, Δt) = \frac{k_{a}}{k_{a} - r} [E_{r} (Δt) - E_{k_{a}} (Δt)]

w_{α} = \frac{α - k_{21}}{α - β}

w_{β} = \frac{k_{21} - β}{α - β}

B_{i} = \frac{F D_{i} \cdot 1000}{V_{c}}

R (Δt) = w_{α} g (α, Δt) + w_{β} g (β, Δt)

C_{i} (t) = B_{i} R (Δt)

The reference-parameter calculation uses this closed-form solution; body-size-adjusted graphs integrate the equivalent differential equations below.

Changing body size — differential equations integrated by the plotter

J = Q (C_{c} - C_{p})

\frac{d A_{d}}{d t} = - k_{a} A_{d}

\frac{d A_{c}}{d t} = F k_{a} A_{d} - CL C_{c} - J

\frac{d A_{p}}{d t} = J

C_{c} = \frac{A_{c}}{V_{c}}

C_{p} = \frac{A_{p}}{V_{p}}

A_{d} (t_{i}^{+}) = A_{d} (t_{i}^{-}) + 1000 D_{i}

The three amount equations use mg-to-µg dose impulses and time-varying CL, Q, Vc, and Vp. The site advances them with one-hour fourth-order Runge–Kutta steps.

Semaglutide — published body-weight covariates and fixed effects

CL = 0.0348 {(\frac{BW}{85})}^{1.01}

Q = 0.304 {(\frac{BW}{85})}^{1.01}

V_{c} = 3.59 {(\frac{BW}{85})}^{0.923}

V_{p} = 4.10 {(\frac{BW}{85})}^{0.923}

F = 0.847

k_{a} = 0.0253 h^{- 1}

The Overgaard et al. rich-sampling model uses an 85 kg reference. Body weight affects clearance, intercompartmental clearance, and both volumes; sex and height were not retained as important semaglutide covariates.

Tirzepatide — published body-size covariates and fixed effects

BMI = \frac{BW}{{(H / 100)}^{2}}

FFM = {\begin{cases} \frac{9270 BW}{6680 + 216 BMI} & male \\ \frac{9270 BW}{8780 + 244 BMI} & female \end{cases}

s_{CL} = {(\frac{BW}{70})}^{0.8}

s_{V} = \frac{FFM + 0.482 (BW - FFM)}{70}

CL = 0.0329 s_{CL}

Q = 0.126 s_{CL}

V_{c} = 2.47 s_{V}

V_{p} = 3.98 s_{V}

F = 0.80

k_{a} = 0.0373 h^{- 1}

FFM = 9270BW/(6680+216BMI) for males or 9270BW/(8780+244BMI) for females. The volume equation is applied to both Vc and Vp.

Default one-compartment parameter reductions

Semaglutide

t_{1 / 2} = 7.37 d

V / F = 12.2 L

k_{a} = 0.0286 h^{- 1}

CL / F = 0.0478 L / h

Tirzepatide

t_{1 / 2} = 5.4 d

V / F = 10.3 L

k_{a} = 0.0373 h^{- 1}

The semaglutide values come from its published phase 3 population model. Tirzepatide uses its population half-life and apparent volume as a transparent reduced model; no overall personal-accuracy percentage is claimed.

Retatrutide surrogate targets

t_{1 / 2} \approx 6 d

V_{z} / F = 7.36 L

k_{a} = 0.08 h^{- 1}

The half-life and mean terminal apparent volume come from phase 1 cohorts. kₐ is fitted so the simplified curve reproduces the observed timing and exposure. Only one-compartment retatrutide plotting is available.

How the compounded tab differs. Compounded semaglutide and tirzepatide run through the same respective model and published parameters as their branded counterparts. This produces a useful reference curve, but assumes brand-like pharmacokinetics that a compounded formulation may not reproduce. Retatrutide uses the one-compartment equation with the explicitly fitted surrogate parameters above.

One-compartment elimination

k_{e} = \frac{\ln (2)}{t_{1 / 2}}

All one-compartment curves derive elimination from the stated half-life after converting days to hours.

Modeled weight

W (t) = \max (0, \frac{t - t_{0}}{168})

L (t) = 0.45359237 W (t)

BW (t) = \max (30, {BW}_{0} - L (t))

Two-compartment mode assumes 1 lb/week loss after the first dose and floors weight at 30 kg.

Dose schedule

t_{base} = (w_{from} - 1) 168 + δ

t_{n} = t_{base} + n (24 I)

t_{n} < 168 w_{to}

δ is 6, 12, or 18 hours for Morning, Afternoon, or Night. I is 7 days normally or the selected compounded interval; doses stop before 168 × “To week.”

Repeated doses

C_{total} (t) = \sum_{i} C_{i} (t)

Every scheduled injection contributes its own curve; Accumulate adds all active regimen curves while Compare displays them separately.

Unit conversion

\frac{1 mg}{1 L} = \frac{1000 ng}{1 mL}

Dose is entered in mg, amount states use µg, volume is in L, and the chart reports ng/mL.

Area under curve

T_{j} = \frac{C_{j - 1} + C_{j}}{2}

AUC \approx \sum_{j = 1}^{N} T_{j} Δt

Δt = 6 h

The displayed AUC uses the trapezoidal rule with six-hour samples.

1
Schedule doses
The selected start date begins at midnight. Morning, Afternoon, and Night map internally to +6, +12, and +18 hours. Standard regimens repeat every 168 hours; a compounded custom interval repeats every X × 24 hours until the end of the selected final week.
2
Apply the weight assumption
In two-compartment mode, modeled weight begins at the entered first-dose weight and decreases continuously by 1 lb per week. To prevent impossible values on very long graphs, the calculation floors modeled weight at 30 kg (66 lb).
3
Sample the timeline
The body-size-adjusted semaglutide and tirzepatide differential equations are integrated in one-hour Runge–Kutta steps. All graph curves and AUC values are retained at six-hour intervals through 1–520 weeks.
4
Accumulate or compare
Accumulate sums the active regimen curves. Compare keeps them as separate lines. Different compounds are never treated as dose-equivalent.
5
Scale and inspect
The y-axis rounds upward to a clean 1–2–5–10 scale above the maximum. Hover and keyboard readings snap to the nearest six-hour sample.

Parameter set

Values used in the code.

Input	Semaglutide	Tirzepatide	Retatrutide
Model structure	One compartment by default; optional two compartments	One compartment by default; optional two compartments	One-compartment surrogate only
Absorption rate kₐ	0.0286 h⁻¹ one-comp; 0.0253 h⁻¹ two-comp	0.0373 h⁻¹	0.08 h⁻¹ fitted
Half-life reference	7.37 days	5.4 days population mean	≈6 days
Bioavailability F	Included in V/F one-comp; 0.847 two-comp	Included in V/F one-comp; 0.80 two-comp	Included in Vz/F
Clearance CL	CL/F 0.0478 L/h one-comp; 0.0348 L/h / 85 kg two-comp	0.0329 L/h / 70 kg two-comp	—
Intercompartmental Q	0.304 L/h / 85 kg	0.126 L/h / 70 kg	—
Central volume Vc	3.59 L / 85 kg	2.47 L / 70 kg	—
Peripheral volume Vp	4.10 L / 85 kg	3.98 L / 70 kg	—
One-compartment V/F	12.2 L	10.3 L	7.36 L cohort mean
Body-size scaling	BW exponent 1.01 for CL/Q; 0.923 for Vc/Vp	BW exponent 0.8 for CL/Q; FFM-adjusted Vc/Vp	None
Model status	Both structures published	Published two-compartment model; transparent one-compartment reduction	Phase 1 fitted surrogate

SEMA

Semaglutide

The default uses the Petri et al. phase 3 one-compartment values: kₐ 0.0286 h⁻¹, CL/F 0.0478 L/h, and V/F 12.2 L. The optional Overgaard et al. rich-sampling two-compartment model uses F 0.847, kₐ 0.0253 h⁻¹, CL 0.0348 L/h, Q 0.304 L/h, Vc 3.59 L, and Vp 4.10 L at 85 kg, with the published body-weight exponents.

TIRZ

Tirzepatide

The default one-compartment reduction uses t½ 5.4 days, V/F 10.3 L, and kₐ 0.0373 h⁻¹. The optional Schneck & Urva two-compartment model uses F 0.80, CL 0.0329 L/h, Q 0.126 L/h, Vc 2.47 L, and Vp 3.98 L at 70 kg, scaling CL/Q with total weight and Vc/Vp with sex-, height-, and BMI-derived fat-free mass.

RETA

Retatrutide

Coskun et al. reported dose-level half-lives of 134–165 hours, T_max values of 12–72 hours, C_max of 110 ng/mL and AUC_0–∞ of 28,300 ng·h/mL at 1 mg, plus Vz/F values across six cohorts. The code uses the approximately six-day half-life, the 7.36 L cohort-mean Vz/F, and fits kₐ to 0.08 h⁻¹. This is a transparent surrogate, not a published population model.

Math checks

Internal and external validation.

✓

Steady-state semaglutide

The default one-compartment model predicts average steady-state concentrations of 62.3 ng/mL at 0.5 mg and 124.5 ng/mL at 1 mg. The Ozempic label reports approximately 65 and 123 ng/mL—differences of 4.2% and 1.2%.

✓

Semaglutide rich-PK model

Automated checks reproduce Overgaard et al.’s two-compartment fixed effects, body-weight exponents, dose proportionality, and expected F·Dose/CL exposure at the 85 kg reference.

✓

Tirzepatide peak timing

The published two-compartment fixed effects predict a single-dose central-plasma peak at 29.6 hours. FDA labeling reports a median of 24 hours and a range of 8–72 hours.

✓

Tirzepatide body-size equations

Automated checks reproduce the 0.8 allometric scaling for CL and Q, the sex-specific fat-free mass equations, and the 0.482 fat-mass fraction used for volumes.

✓

One- versus two-compartment

At 5 mg and the fixed 70 kg tirzepatide reference, the one-compartment option peaks at 350.7 ng/mL after 60.8 hours versus 515.0 ng/mL after 29.6 hours for the two-compartment model. This compares structures, not personal accuracy.

✓

Dose proportionality

The equation is linear in dose: doubling a dose doubles every concentration and AUC value. That matches the dose-proportional exposure reported for semaglutide, tirzepatide, and retatrutide.

✓

Accumulation behavior

Repeated weekly doses approach a plateau over roughly 4–5 half-lives. This matches labeled steady state at 4–5 weeks for semaglutide and 4 weeks for tirzepatide.

✓

Dose-time scheduling

Automated checks confirm that a dose contributes zero before its selected Morning, Afternoon, or Night offset and begins contributing after that scheduled point.

✓

Custom interval scheduling

Automated checks confirm that compounded schedules repeat at the selected whole-day interval and stop before the week following the chosen “To week.”

✓

Retatrutide phase 1 fit

At 1 mg, the surrogate predicts T_max 37.4 hours, C_max 113.5 ng/mL, and AUC 28,227 ng·h/mL. Phase 1 observations were 12–72 hours overall, 110 ng/mL, and 28,300 ng·h/mL.

Automated calculation checkstwo published semaglutide structuresbody-size covariates1 lb/week assumptiontwo-compartment AUC balance

Model limits

What this cannot tell you.

Actual exposure varies with body size, injection timing and site, formulation, adherence, individual clearance, assay method, and other clinical factors. The optional body-size inputs refine population-model parameters but do not identify an individual’s true pharmacokinetics.

Not a measured level. The tooltip is a population-model estimate, not a laboratory result.
Body-size adjusted, not individualized PK. Weight, height, and sex adjust the published typical parameters; unexplained interindividual and residual variability remain.
Weight history is assumed. Two-compartment mode assumes exactly 1 lb of loss per week after the first dose and floors modeled weight at 30 kg. Real weight trajectories vary, plateau, or reverse.
Semaglutide weight change is extrapolated. Overgaard et al. assessed body weight as a baseline covariate. Reapplying its weight equations along the assumed 1 lb/week path is a transparent site assumption, not a directly validated longitudinal semaglutide model.
Semaglutide reference choices are fixed. The optional curve uses the paper’s healthy-reference, 1.34 mg/mL product-strength fixed effects because the form does not ask for glycaemic status or product concentration.
Semaglutide covariates differ. The published semaglutide model retained body weight as the important covariate; sex and height are collected because they are required by tirzepatide’s fat-free-mass equation, not because they improve semaglutide parameters.
No model-accuracy percentage. The sources do not report one universal personal-accuracy score, so the site does not invent one.
Not dose equivalence. Adding semaglutide and tirzepatide concentrations is a mass visualization only and does not imply equal effect or safety.
Custom intervals are descriptive only. The compounded control models the schedule entered; it does not establish that the interval is appropriate or safe.
Not oral semaglutide. Rybelsus and Wegovy tablets use daily oral dosing with highly condition-dependent bioavailability, so they are outside this injected-dose model.
Compounded products are not FDA approved. Their formulation, labeled concentration, absorption, quality, and bioavailability can differ. The compounded semaglutide and tirzepatide curves assume the published brand-name parameters and may not represent a particular vial.
Retatrutide is investigational. FDA states it cannot be used in compounding under federal law. Its curve is a simplified fit to phase 1 human PK, not an approved dosing model or support for use or sourcing.
Not treatment advice. Do not use the graph to start, stop, combine, or change medication. Ask a licensed clinician or pharmacist.

Evidence base

Primary sources

FDA labels establish approved dose strengths and observed clinical PK. Peer-reviewed population analyses supply model parameters, and the retatrutide phase 1 trial supplies the surrogate-fitting targets. The FDA notice establishes current compounding and approval status.