Method and parameters
Every number on this site comes from the equations below and the constants in the table. Nothing is estimated by a language model, and nothing is copied from another calculator. If a figure here is wrong, it is wrong in a way you can check, which is the point of publishing this page.
Concentration over time
Drug amount is modelled with a one-compartment model with first-order absorption, the Bateman function. For a single dose:
A(t) = (F · D · ka) / (ka − ke) · (e^(−ke·t) − e^(−ka·t))
- A(t)
- amount in the body at time t, in milligrams
- F
- bioavailability, the fraction absorbed after a subcutaneous injection
- D
- dose administered, in milligrams
- ka
- absorption rate constant, per hour
- ke
- elimination rate constant, ln(2) divided by the half life in hours
Plasma concentration is this divided by the volume of distribution. We report amount rather than concentration because it is what people are actually asking about, and because it does not require the reader to know their own volume of distribution.
Multiple doses are handled by superposition. At each time point the model computes what remains of every prior dose and sums them. The simulation runs at 30-minute resolution. When ka and ke are equal the equation above divides by zero, so the model uses the analytic limit, A(t) = F · D · ka · t · e^(−ka·t), instead.
Constants
| Compound | Half life | ke (/h) | ka (/h) | Tmax | F | Vd (L) |
|---|---|---|---|---|---|---|
| Retatrutide | 6 d | 0.004814 | 0.055 | 48.5 h | 0.95 | 7 |
| Tirzepatide | 5 d | 0.005776 | 0.14 | 23.8 h | 0.8 | 10.3 |
| Semaglutide | 7 d | 0.004126 | 0.06 | 47.9 h | 0.89 | 12.5 |
How ka was chosen
Absorption rate is rarely published directly, so each one is solved from the compound's reported time to peak by inverting the Bateman function:
Tmax = ln(ka / ke) / (ka − ke)
The Tmax column above is that equation run forwards again on our own constants, so it should match the published figure for each compound. A test in the build asserts each one lands within three hours of its documented value, which means this table cannot silently drift.
This is worth stating plainly because it is where we differ from other calculators in this space. At least one widely used tool publishes a single absorption rate of 0.5 per hour for all three compounds. That implies an absorption half life of about 1.4 hours and a peak roughly nine hours after injection, which contradicts the published pharmacokinetics for every one of them, and contradicts that tool's own description of a peak arriving a day or two later.
Derived figures
| Figure | Definition |
|---|---|
| Peak | The maximum of the summed curve across the whole simulation. |
| Trough | The amount immediately before each injection. |
| Steady state | The first dose at which the trough differs from the previous trough by less than one percent. An escalating titration never satisfies this, and the model reports that honestly rather than picking a number. |
| Out of system | The first time after the last dose that the amount falls below 0.02 mg. This threshold is a display convention, not a clinical one. |
Reconstitution
concentration (mg/mL) = vial mg / bacteriostatic water mL volume (mL) = dose mg / concentration units = volume mL × units per mL of the syringe
Units per millilitre is 100 on a standard U-100 insulin syringe and 40 on a U-40. Doses per vial is the vial's milligrams divided by the dose, rounded down: the remainder cannot make up a full dose and is reported separately rather than quietly ignored.
Storage windows
These are commonly cited general references, not manufacturer claims for any specific product. They are inputs you can change, and the calculator reports which window it used alongside every result.
| Diluent | Storage | Days | Basis |
|---|---|---|---|
| bacteriostatic | refrigerated | 28 | Common conservative reference for benzyl-alcohol-preserved diluent |
| bacteriostatic | room | 2 | Common reference for unrefrigerated preserved solution |
| sterile | refrigerated | 1 | Unpreserved diluent. Single use, discard same day |
| sterile | room | 0 | Unpreserved and unrefrigerated. Use immediately |
Time spent out of the fridge is charged against the refrigerated budget at the ratio of the two windows. With a 28 day refrigerated window against a 2 day room temperature window that ratio is 14, so six hours at room temperature costs about 3.5 days of shelf life.
What this model does not do
Stating the limits is part of the method. A model that claims no error is not being honest about what it is.
- It is a one-compartment fit. Real distribution is multi-compartment, so the early part of the curve after each injection is a simplification.
- Constants are population averages. Individual clearance varies with body weight, renal function, age and other factors the model does not take as inputs.
- It models the amount of compound present, not effect. Appetite suppression, side effects and weight change do not track the curve one to one.
- Retatrutide constants come from published trial pharmacokinetics. It is an investigational compound and those figures may be revised.
- Reconstitution maths assumes the label is accurate and the compound fully dissolves. Neither is verifiable from a calculator.
Corrections
If a constant or an equation here is wrong, it is wrong on thousands of pages at once, so we would rather hear about it than not. Send a correction with a source and we will publish the change and the date.