dilutioncalculator.co.uk§ Verified 20 Jun 2026 · Reviewed by A. Hargreaves, MChem (Hons)

C₁V₁=C₂V₂ calculator

Lab-grade stock-to-working dilution. Enter any three of stock concentration, stock volume, target concentration, and target volume. The calculator solves the fourth.

§ MeasureDesk
Concentrate
76.9 ml
Water
4 923.1 ml
Total at strength
5 000 ml
1.54 % v/v
§ PourScale · true-to-ratio
concentrate 1.54 %water 98.46 %

§ 1The formula

C₁V₁ = C₂V₂. C is concentration, V is volume. Index 1 is stock, index 2 is the working solution. Units must match within each side: M with M, mM with mM, ml with ml. The formula is unitless if both sides match.[14]

§ 2Worked example · 1 M to 50 mM in 100 ml

  1. Convert to common units. 50 mM = 0.05 M.
  2. V₁ = (C₂ × V₂) ÷ C₁ = (0.05 × 100) ÷ 1 = 5 ml of stock.
  3. Add 5 ml of 1 M stock to a 100 ml volumetric flask. Top up with diluent to 100 ml.
  4. Mix by inversion. Final = 50 mM in 100 ml.

§ 3When it breaks down

  • Non-ideal mixing. Ethanol-water blends contract on mixing; 50 ml ethanol + 50 ml water gives less than 100 ml. Use mass-based blending for ethanol over 30 % v/v.
  • Partial volumes. Concentrated H₂SO₄ released at 98 % w/w has density 1.84 g/ml; assume volumes carry through is wrong without a density correction.
  • Hydrate water of crystallisation. A 1 M CuSO₄·5H₂O stock by formula weight differs from a CuSO₄ anhydrous calculation by 36 %.

§ 4Related