Dilution Calculator

The dilution formula is C₁V₁ = C₂V₂, where C₁ is the initial concentration of the stock solution, V₁ is the volume of stock taken, C₂ is the target (final) concentration, and V₂ is the total final volume. The equation expresses conservation of moles: the number of moles of solute is the same before and after dilution (you add solvent, not more solute).

Example: prepare 500 mL of 0.1 M NaCl from a 5 M stock. Use C₁V₁ = C₂V₂: 5 × V₁ = 0.1 × 0.5, so V₁ = 0.05 / 5 = 0.01 L = 10 mL. Measure 10 mL of the 5 M stock, transfer it to a 500 mL volumetric flask, and add distilled water to the 500 mL mark. The volume of solvent added is 500 − 10 = 490 mL.

The dilution factor (DF) is the ratio of final volume to initial volume: DF = V₂ / V₁. A 1:10 dilution has DF = 10 (1 part sample in 10 parts total, adding 9 parts solvent). A 1:5 dilution has DF = 5. For a series of dilutions with the same DF, the overall factor after n steps is DF^n. The final concentration equals C₁ / DF^n.

A serial dilution is a stepwise series of dilutions, each by the same factor (typically 2× or 10×). Each step dilutes the previous diluted solution, not the original stock. After n steps of factor f, the concentration is C₀ / f^n. Serial dilutions are used in microbiology (bacterial counting), pharmacology (dose-response curves), and serology (antibody titration) to create a geometric progression of concentrations.

Yes - C₁V₁ = C₂V₂ applies to any concentration unit, as long as C₁ and C₂ use the same unit. It works for molarity (M), percent (w/v, v/v), mg/mL, ppm, ppb, or any other concentration expression. The equation simply says that the total amount of solute is conserved. The volumes must also use the same unit (both mL, both L, etc.).

After computing V₂ using C₁V₁ = C₂V₂, the volume of solvent to add is simply V_solvent = V₂ − V₁. Example: if V₁ = 10 mL (stock volume taken) and V₂ = 500 mL (required final volume), add 500 − 10 = 490 mL of solvent. Note: always add stock to solvent (especially for concentrated acids) to control heat of mixing safely.

Dilution factor (DF = V₂/V₁) is always ≥ 1 and describes how many times more dilute the solution becomes. Concentration factor is its inverse (V₁/V₂ ≤ 1). A DF of 10 means the final concentration is 1/10 of the stock. A concentration factor of 5 (not a dilution) would mean the final concentration is 5× the stock - achieved by evaporation, not by adding solvent.

In a titration ELISA or agglutination assay, a serum sample is diluted serially (e.g., 2× steps: 1:2, 1:4, 1:8, 1:16, ...). The titer is reported as the highest dilution that still gives a positive result. If a sample is positive at 1:128 but negative at 1:256, the titer is 1:128 (DF = 128). This calculator's serial dilution table shows all concentrations so you can plan your dilution scheme.

Molarity (M) is moles of solute per litre of solution. When you dilute from C₁ to C₂: C₂ = C₁ × V₁ / V₂. Example: 50 mL of 2 M HCl diluted to 200 mL: C₂ = 2 × 50/200 = 0.5 M. Use the Molarity Calculator to first find C₁ if you only know the mass and molar mass of your solute.

Always add acid to water, never water to acid. Concentrated sulfuric acid (H₂SO₄) releases significant heat when mixed with water - adding water to concentrated acid can cause violent spattering. Procedure: fill the container partly with water, then slowly add acid while stirring. Allow to cool between additions. This applies to H₂SO₄, HCl, HNO₃, and other concentrated acids.

The equation assumes ideal behavior: no volume contraction or expansion when mixing, and no chemical reaction between solute and solvent. For most dilutions with water (especially dilute solutions), the approximation is excellent. For concentrated solutions of strong electrolytes or alcohols, there can be slight volume changes (e.g., ethanol + water contracts by up to 3%). For high-precision work, prepare dilutions gravimetrically (by mass) and measure density.