Cmax is the maximum (peak) serum concentration of a drug after a dose. It determines how intense the peak effect is, including peak side effects. For testosterone cypionate injected weekly, Cmax occurs roughly 2-3 days post-injection; for semaglutide, Cmax is at 1-3 days; for a subcutaneous peptide like BPC-157, Cmax is within minutes.

What is half-life and why does it matter?

Half-life (t½) is the time it takes for the serum concentration to drop by 50% after absorption is complete. It dictates (1) how often you need to dose to maintain steady serum levels, (2) how long it takes to reach steady state (~5 × t½), and (3) how long a drug lingers after discontinuation (~5 × t½ to be effectively cleared). Testosterone cypionate t½ ≈ 8 days; semaglutide t½ ≈ 7 days; BPC-157 extrapolated t½ ≈ 1-2 h.

Why does it take five half-lives to reach steady state?

Each half-life period, the gap between current concentration and the steady-state target is halved. After 1 t½ you're 50% of the way there; 2 t½ = 75%; 3 t½ = 87.5%; 4 t½ = 94%; 5 t½ = 97%. Five is the convention because 97% is indistinguishable from 100% clinically. For testosterone cypionate (t½ ≈ 8 days), steady state takes approximately 40 days. For semaglutide (t½ ≈ 7 days), approximately 35 days.

What is the Bateman equation?

The Bateman equation models the serum concentration of a drug over time after a single extravascular dose (oral, subcutaneous, or intramuscular) in a one-compartment model with first-order absorption. The formula is C(t) = (F·D·ka)/(V·(ka − ke)) · (e^(−ke·t) − e^(−ka·t)), where F is bioavailability, D is dose, ka is absorption rate, ke is elimination rate, V is volume of distribution. It underlies the PK simulation in VitaLog for most compounds.

AUC is area under the concentration-vs-time curve, total drug exposure across the dosing interval. A higher AUC means more total drug effect; an equal AUC from two different regimens produces approximately equal overall exposure regardless of how the peaks and troughs compare. AUC is a primary measure of bioavailability and is frequently cited in label information and bioequivalence studies.

What's the difference between one-compartment and two-compartment models?

A one-compartment model assumes the drug distributes instantaneously into a single body pool and is eliminated from that pool at a first-order rate. It's a good approximation for most subcutaneous peptides, oral orals, and most injectable esters. A two-compartment model explicitly separates a fast-equilibrating central compartment (blood) from a slower-equilibrating peripheral compartment (tissue), producing a biphasic curve. Testosterone base/suspension fits two-compartment kinetics; most other TRT esters fit one-compartment closely enough.

What does accumulation ratio mean?

When you dose repeatedly at an interval shorter than 5 × t½, each dose adds onto the residue of previous doses. Accumulation ratio is how much higher the steady-state average serum concentration is compared to a single-dose average. Formula: 1 / (1 − e^(−ke·τ)). For testosterone cypionate weekly (τ ≈ 1 × t½), accumulation is ~2×. For semaglutide weekly (τ ≈ 1 × t½ too), accumulation is ~2×. For daily dosing of a 24 h t½ drug, τ = t½, accumulation ≈ 2.0. High accumulation means longer time to steady state but flatter peak-trough ratio once you're there.

How do variability envelopes work?

Two people taking the same dose of the same drug don't always have the same serum concentration, absorption rate, clearance, and volume of distribution all vary. VitaLog's PK simulator computes a P25-P75 envelope (interquartile range) using log-normal coefficient-of-variation multipliers: factor = exp(±0.6745 × σ), σ = √(ln(1 + CV²)). For testosterone cypionate the inter-individual CV on clearance is around 20-30%, giving a visible band of expected values around the mean curve.

Why does VitaLog plot a curve instead of just telling me a number?

A single 'Cmax 980 ng/dL' number hides the shape. The curve shows (a) where in the dosing interval you'd draw for trough vs peak, (b) how long after injection the peak occurs (can you feel 'worse' on day 3?), (c) whether accumulation is still building toward steady state, and (d) how a different ester or frequency would change the picture. All four are useful for decisions about dose, frequency, and bloodwork timing.

Is this medical advice?

No. Pharmacokinetics is the physics of drugs in the body, this guide explains the concepts. It does not tell you what dose to take, which drug to use, or how to interpret your specific response. For prescribing decisions, consult a qualified healthcare professional.

Pharmacokinetics Explained: Cmax, Half-Life, AUC & Steady State Without the Math PhD

The physics of drugs in the body, in plain English, aimed at athletes on TRT, peptide users, GLP-1 patients, and anyone trying to understand what their PK simulator is showing them.

Last updated: 2026-04-21 · Maintained by the VitaLog team

TL;DR. Five numbers govern every drug's serum curve: Cmax (peak), Tmax (time to peak), t½ (half-life), AUC (total exposure), and Css (steady-state average). You reach steady state after ~5 half-lives of repeated dosing. If you dose more often than one half-life, your drug accumulates. This is the entire framework for reasoning about testosterone esters, GLP-1s, peptides, and most other compounds.

The five numbers that matter

Pharmacokinetics has thousands of papers and dozens of mathematical models. For clinical reasoning, almost everything reduces to five numbers:

Number	What it is	Why it matters
Cmax	Maximum (peak) serum concentration	Determines peak effect and peak side effects
Tmax	Time from dose to Cmax	Tells you when peak effects occur ("why do I feel off on day 3?")
t½ (half-life)	Time for concentration to halve	Governs dosing frequency, time to steady state, and time to wash-out
AUC	Area under concentration-time curve	Total exposure, primary measure of bioavailability
Css (steady state)	Average serum concentration once input = elimination	What you "run at" on a chronic protocol

That's the whole framework. Everything else, Bateman, two-compartment, flip-flop kinetics, accumulation ratios, is how we compute these five numbers from lab parameters.

Half-life and why five of them = steady state

Half-life is the time it takes for serum concentration to drop by 50% after absorption is complete. It's governed by the first-order elimination rate constant ke: t½ = ln(2) / ke ≈ 0.693 / ke.

When you start a chronic dosing schedule (say, weekly testosterone cypionate), serum concentration climbs toward a steady-state plateau. Each half-life period closes 50% of the remaining gap to that plateau:

Half-lives elapsed:  1    2    3    4    5
% of steady state:  50%  75%  87.5%  94%  97%

After five half-lives, you're at 97% of steady state, clinically indistinguishable from 100%. That's why the convention is "5 × t½ to reach steady state."

Real-world numbers:

Testosterone cypionate (t½ ≈ 8 days) → steady state at ~40 days (6 weeks)
Testosterone enanthate (t½ ≈ 4.5 days) → steady state at ~23 days (3.5 weeks)
Testosterone propionate (t½ ≈ 0.8 days) → steady state at ~4 days
Semaglutide (t½ ≈ 7 days) → steady state at ~35 days (5 weeks)
BPC-157 (t½ ≈ 1-2 h, extrapolated from animal models, no human PK data published) → steady state at ~10 h (intra-day, not meaningful)

The Bateman equation

When you inject a drug subcutaneously or intramuscularly, serum concentration rises as drug absorbs from the injection site and then falls as the body eliminates it. The curve is described by the Bateman equation:

C(t) = (F · D · ka) / (V · (ka − ke)) · (e^(−ke·t) − e^(−ka·t))

Where:
  C(t) = serum concentration at time t
  F    = bioavailability (fraction of dose reaching systemic circulation)
  D    = dose (in mass units)
  ka   = absorption rate constant
  ke   = elimination rate constant
  V    = volume of distribution

The exponential terms compete: e^(−ka·t) describes drug being absorbed out of the injection depot, and e^(−ke·t) describes drug being eliminated from blood. At t = 0, both terms equal 1 and C = 0. As t increases, the absorption term goes to zero first (for most drugs ka > ke), leaving the elimination term, the familiar exponential decay from Cmax.

Cmax occurs at Tmax, where dC/dt = 0:

Tmax = ln(ka/ke) / (ka − ke)

Flip-flop tip. For very slow-absorbing depot formulations (nandrolone decanoate, testosterone undecanoate), ka can be smaller than ke. Then the apparent terminal half-life in the blood is governed by ka, not ke, the depot is releasing drug so slowly that it looks like slow elimination. VitaLog handles both orderings automatically.

One-compartment vs. two-compartment models

The Bateman equation above is a one-compartment model: it assumes the drug instantly distributes into a single body pool (blood + tissue treated as one) and is eliminated at a single first-order rate. Good approximation for most subcutaneous peptides and slow-release injectable esters.

A two-compartment model adds a peripheral (tissue) compartment that drug enters and leaves from the central (blood) compartment at different rates. Now the curve has two distinct phases:

α phase (distribution): rapid early decline as drug moves from blood into tissue.
β phase (elimination): slower terminal decline as drug leaves both compartments.

Testosterone base (suspension) shows classical two-compartment behavior, the rapid IV Cmax is quickly blunted by tissue distribution, then the real elimination t½ emerges. Most TRT esters are slow enough to absorb that the distribution phase is masked and one-compartment is fine.

VitaLog's PK engine picks the correct model per compound: one-compartment for most peptides and esters, two-compartment for testosterone suspension, biphasic one-compartment sum for depot formulations with distinct fast + slow absorption phases.

Accumulation: why weekly dosing stacks

If you inject weekly and your drug has a weekly half-life, each injection lands on top of meaningful residue from previous injections. The steady-state average is higher than a single-dose average by the accumulation ratio:

Accumulation ratio = 1 / (1 − e^(−ke·τ))

where τ = dosing interval

Worked examples:

τ = t½ (daily dose of a 24 h t½ drug) → ratio = 2.0 (you end up at 2× single-dose average)
τ = 0.5 × t½ (dosing twice per half-life) → ratio = 3.4
τ = 2 × t½ (dosing every two half-lives) → ratio = 1.33
τ = 5 × t½ (infrequent dosing) → ratio ≈ 1.03 (effectively no accumulation)

Testosterone cypionate at weekly intervals has τ ≈ t½, so accumulation ≈ 2. Semaglutide weekly is the same shape: t½ ≈ 7 d and τ = 7 d, giving accumulation ≈ 2× (formula: 1/(1−e^{−ln 2}) = 2.0 exactly). The reason semaglutide feels so smooth at steady state isn't a huge multiplier, it's that the ~7-day half-life already makes the within-week peak-trough ratio small, and the 2× accumulation further flattens it.

Why the P25-P75 envelope matters

Your friend takes 200 mg testosterone cypionate weekly and has a trough of 650 ng/dL. You take the same dose and have a trough of 420 ng/dL. Both normal, people differ in absorption rate, clearance, and volume of distribution.

VitaLog's PK simulator computes a P25-P75 envelope (interquartile band) around every curve, using log-normal coefficient-of-variation multipliers derived from population-PK studies:

factor = exp(±0.6745 × σ)
σ      = √(ln(1 + CV²))

For testosterone cypionate, inter-individual CV on clearance is approximately 20-30%, which produces a visibly wide band. This matters because a single target serum concentration is not a goal, a range is. Your "optimal dose" is whatever places you comfortably inside a healthy range at trough, not whatever matches your friend's trough.

Five real examples

1. Testosterone cypionate, 200 mg/week IM

t½ ≈ 8 days
Cmax ≈ 1,200 ng/dL at Tmax ≈ 2-3 days
Cmin ≈ 500 ng/dL at day 7
Steady state at ~6 weeks
Accumulation ratio ≈ 2×

2. Semaglutide, 1 mg/week subcutaneous

t½ ≈ 7 days
Cmax ≈ 55-75 ng/mL at steady state, Tmax ≈ 1-3 days post-injection
Cmin ≈ 40-55 ng/mL at day 7
Steady state at ~5 weeks
Accumulation ratio ≈ 2× (τ ≈ t½ gives ratio = 1/(1 − e^−ln(2)) = 2.0)

3. BPC-157, 250 mcg/day subcutaneous

t½ extrapolated from animal data ≈ 1-2 h
Cmax within minutes; daily dosing is punctate, not accumulating
Steady-state concept doesn't really apply, each day is an isolated pulse

4. Anavar (oxandrolone), 40 mg/day oral

t½ ≈ 9 h
Tmax ≈ 1 h post-ingestion
Twice-daily dosing (20 mg BID) gives smoother serum levels than once-daily
Accumulation ratio ≈ 1.9 for BID dosing (τ = 12 h ≈ 1.3 × t½)

5. Tirzepatide, 5 mg/week subcutaneous

t½ ≈ 5 days
Weekly dosing like semaglutide but slightly shorter half-life
Steady state at ~25 days (3.5 weeks)
Accumulation ratio ≈ 1.6× (τ = 7 days, t½ = 5 days → ke·τ = ln(2)·7/5 ≈ 0.97 → 1/(1 − e^−0.97) ≈ 1.61)

Using the VitaLog PK simulator

In the app: pick a compound, enter your dose + frequency, and the simulator plots the full serum curve with the P25-P75 envelope, Cmax/Tmax annotations, and horizontal reference-range bands (where applicable). Change the ester or frequency and watch the curve update in real time. Pair with your bloodwork trends to see whether your actual trough lines up with the modeled trough.

Run a PK simulation in VitaLog

Visualize any of 330 compounds' serum curves with published Cmax/Tmax/t½ + variability envelope. Sign up free to save protocols against your bloodwork; no signup needed to play with the simulator.

Open the PK simulator (no signup) Save to my protocol

Frequently asked questions

What is Cmax?: Cmax is the maximum (peak) serum concentration of a drug after a dose. It determines how intense the peak effect is, including peak side effects. For testosterone cypionate injected weekly, Cmax occurs roughly 2-3 days post-injection; for semaglutide, Cmax is at 1-3 days; for a subcutaneous peptide like BPC-157, Cmax is within minutes.
What is half-life and why does it matter?: Half-life (t½) is the time it takes for the serum concentration to drop by 50% after absorption is complete. It dictates (1) how often you need to dose to maintain steady serum levels, (2) how long it takes to reach steady state (~5 × t½), and (3) how long a drug lingers after discontinuation (~5 × t½ to be effectively cleared). Testosterone cypionate t½ ≈ 8 days; semaglutide t½ ≈ 7 days; BPC-157 extrapolated t½ ≈ 1-2 h.
Why does it take five half-lives to reach steady state?: Each half-life period, the gap between current concentration and the steady-state target is halved. After 1 t½ you're 50% of the way there; 2 t½ = 75%; 3 t½ = 87.5%; 4 t½ = 94%; 5 t½ = 97%. Five is the convention because 97% is indistinguishable from 100% clinically. For testosterone cypionate (t½ ≈ 8 days), steady state takes approximately 40 days. For semaglutide (t½ ≈ 7 days), approximately 35 days.
What is the Bateman equation?: The Bateman equation models the serum concentration of a drug over time after a single extravascular dose (oral, subcutaneous, or intramuscular) in a one-compartment model with first-order absorption. The formula is C(t) = (F·D·ka)/(V·(ka − ke)) · (e^(−ke·t) − e^(−ka·t)), where F is bioavailability, D is dose, ka is absorption rate, ke is elimination rate, V is volume of distribution. It underlies the PK simulation in VitaLog for most compounds.
What is AUC?: AUC is area under the concentration-vs-time curve, total drug exposure across the dosing interval. A higher AUC means more total drug effect; an equal AUC from two different regimens produces approximately equal overall exposure regardless of how the peaks and troughs compare. AUC is a primary measure of bioavailability and is frequently cited in label information and bioequivalence studies.
What's the difference between one-compartment and two-compartment models?: A one-compartment model assumes the drug distributes instantaneously into a single body pool and is eliminated from that pool at a first-order rate. It's a good approximation for most subcutaneous peptides, oral orals, and most injectable esters. A two-compartment model explicitly separates a fast-equilibrating central compartment (blood) from a slower-equilibrating peripheral compartment (tissue), producing a biphasic curve. Testosterone base/suspension fits two-compartment kinetics; most other TRT esters fit one-compartment closely enough.
What does accumulation ratio mean?: When you dose repeatedly at an interval shorter than 5 × t½, each dose adds onto the residue of previous doses. Accumulation ratio is how much higher the steady-state average serum concentration is compared to a single-dose average. Formula: 1 / (1 − e^(−ke·τ)). For testosterone cypionate weekly (τ ≈ 1 × t½), accumulation is ~2×. For semaglutide weekly (τ ≈ 1 × t½ too), accumulation is ~2×. For daily dosing of a 24 h t½ drug, τ = t½, accumulation ≈ 2.0. High accumulation means longer time to steady state but flatter peak-trough ratio once you're there.
How do variability envelopes work?: Two people taking the same dose of the same drug don't always have the same serum concentration, absorption rate, clearance, and volume of distribution all vary. VitaLog's PK simulator computes a P25-P75 envelope (interquartile range) using log-normal coefficient-of-variation multipliers: factor = exp(±0.6745 × σ), σ = √(ln(1 + CV²)). For testosterone cypionate the inter-individual CV on clearance is around 20-30%, giving a visible band of expected values around the mean curve.
Why does VitaLog plot a curve instead of just telling me a number?: A single "Cmax 980 ng/dL" number hides the shape. The curve shows (a) where in the dosing interval you'd draw for trough vs peak, (b) how long after injection the peak occurs (can you feel "worse" on day 3?), (c) whether accumulation is still building toward steady state, and (d) how a different ester or frequency would change the picture. All four are useful for decisions about dose, frequency, and bloodwork timing.
Is this medical advice?: No. Pharmacokinetics is the physics of drugs in the body, this guide explains the concepts. It does not tell you what dose to take, which drug to use, or how to interpret your specific response. For prescribing decisions, consult a qualified healthcare professional.

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Pharmacokinetics Explained: Cmax, Half-Life, AUC & Steady State Without the Math PhD

The five numbers that matter

Half-life and why five of them = steady state

The Bateman equation

One-compartment vs. two-compartment models

Accumulation: why weekly dosing stacks

Why the P25-P75 envelope matters

Five real examples

1. Testosterone cypionate, 200 mg/week IM

2. Semaglutide, 1 mg/week subcutaneous

3. BPC-157, 250 mcg/day subcutaneous

4. Anavar (oxandrolone), 40 mg/day oral

5. Tirzepatide, 5 mg/week subcutaneous

Using the VitaLog PK simulator

Run a PK simulation in VitaLog

Frequently asked questions

Related resources