Exam aid · Calculations and formulas

PK & Calculation Formulas

One page of formulas for PK and dispensing calculations, with the units that trip people up.

Tables to memorise

Cover the right-hand column and test yourself before checking.

Quantity	Formula
Half-life	t½ = 0.693 / k = 0.693 × Vd / CL
Clearance	CL = k × Vd = Dose × F / AUC
Volume of distribution	Vd = Dose / C0 (IV bolus)
Loading dose	LD = Vd × Ctarget / F
Maintenance dose rate	Rate = CL × Css / F
Average Css (oral)	Css,avg = F × Dose / (CL × τ)
Accumulation factor	R = 1 / (1 − e^(−kτ)); = 2 when τ = t½
Absolute bioavailability	F = (AUCoral/Doseoral) ÷ (AUCiv/Doseiv)
Organ clearance	CL = Q × E (blood flow × extraction ratio)
Time to steady state	4–5 half-lives (90% at 3.3 t½)
Michaelis–Menten (phenytoin)	Dose = Vmax × Css / (Km + Css)

Quantity	Formula
Dilution	C1 × V1 = C2 × V2
% w/v	grams per 100 mL
1 in X	1 g in X mL (1 in 1000 = 1 mg/mL)
mmol	mg ÷ molecular weight
mEq	mmol × valency
mOsm/L	mmol/L × number of particles
Drip rate	Volume (mL) × drop factor ÷ time (min)
Isotonicity (E value)	NaCl to add = 0.9 g/100 mL − Σ(drug g × E)
Freezing point method	Isotonic = −0.52 °C depression
Alligation	Parts = difference between the other strength and the target
Displacement value	Base displaced = drug weight ÷ DV

Loading dose depends on Vd; maintenance dose depends on clearance.
Half-life changes only if Vd or CL changes; dose does not change it (first order).
Time to steady state depends only on half-life, not on dose or loading.
1 in 1000 adrenaline = 1 mg/mL (IM anaphylaxis); 1 in 10,000 = 0.1 mg/mL (IV arrest).
0.9% NaCl ≈ 154 mmol/L Na⁺ ≈ 308 mOsm/L.
Hausner ratio above 1.25 or Carr's index above 25% means poor flow.

Load the Volume, Maintain the Clearance: LD = Vd × C; maintenance rate = CL × Css.
0.105 for 90%: First-order shelf life t90 = 0.105/k (ln 100/90 = 0.105).

Attempt MCQs on these topics while the sheet is fresh. Anything you get wrong goes to your incorrect list for the next round.