Steady-State Dosing: Single vs Split

Why dividing a daily dose smooths the curve but leaves average exposure unchanged.

If a 24-hour schedule repeats forever, the body never starts empty. Each cycle begins with leftover drug from all previous cycles, and the curve settles into a repeating steady state where the amount at t = 0 equals the amount at t = 24.

The carryover

A recurring dose D given once per period T builds up to the geometric sum of all past administrations:

peakss = D / (1 − e−kT)

Here e−24k = 0.0929, so the carryover multiplier is 1 / (1 − 0.0929) ≈ 1.10 — every dose effectively sits on ~10% extra residual.

The headline result

At steady state both schedules have the exact same 24-hour average, because

average = (total daily dose) / (k · T) = 200 / (0.0990 × 24) ≈ 84.2 mg

It depends only on the total daily dose and the half-life — not on whether you split it or when you take it.

Adjust the half-life

7 hr

Drag to see how clearance speed reshapes the curves, the carryover, and the 24-hour average.

Steady-state curves over one 24-hour cycle

Single 200 mg Split 100 + 100 mg Average 84.2 mg

So at steady state

Single 200 mgSplit 100 + 100 mg
24-h average84.2 mg84.2 mg
Peak220 mg171 mg
Trough20.5 mg28.8 mg
Swing (range)200 mg142 mg

Both schedules sit at the same 84.2 mg average, and neither touches zero — the single dose falls to 20.5 mg at its trough, the split to 28.8 mg. The carryover from previous cycles is what lifts the whole curve up.

The only real difference is fluctuation. The single 200 mg dose swings across a 200 mg range (20.5 → 220 mg), while splitting it into 100 + 100 mg shrinks the swing to 142 mg (28.8 → 171 mg). That's the entire pharmacological point of dividing a daily dose: the average exposure is fixed by how much you take and how fast you clear it, but spreading the doses out smooths the peaks and troughs.

Notes on the model

The split doses sit at the t = 6 and t = 12 phases, but since it's now a cycle the phase is arbitrary — sliding both schedules earlier or later just shifts the curves sideways without changing the average or the swing.

This assumes instant absorption; a real oral tablet absorbs over an hour or two, which would round off the sharp peaks a little but leave the averages untouched. (k = 0.0990 hr−1, half-life = 7 hr.)