Solution Dilution Calculator

Five dilution scenarios in one place — select what you are trying to do and the right calculator appears below.

What are you trying to do?

Classic Dilution — C₁V₁ = C₂V₂

C₁ × V₁ = C₂ × V₂

You have a stock solution and want to make a working solution. Enter any three values and choose which variable to solve for.

Solve for:

C₁ — Stock concentration

V₁ — Volume of stock to use

C₂ — Desired concentration

V₂ — Final (total) volume

Result

C₁V₁ = C₂V₂ | C₁ = stock conc. · V₁ = volume of stock taken · C₂ = desired conc. · V₂ = final total volume
Volume of diluent to add = V₂ − V₁

Spike into Existing Solution

(Mₚ × Vₚ) + (Mₛ × Vₓ) = Mf × (Vₚ + Vₓ)

You already have a solution and want to raise its concentration by adding stock directly. Solves for Vₓ — the volume of stock to spike in.

Mₚ — Present concentrationCurrent conc. of your existing solution

Vₚ — Present volumeVolume already in your tube/flask

Mₛ — Stock concentrationConc. of the stock you will spike in

Mf — Desired final concentrationTarget conc. after spiking

Volume of stock to add (Vₓ)

(Mₚ × Vₚ) + (Mₛ × Vₓ) = Mf × (Vₚ + Vₓ)
Solved for Vₓ: Vₓ = Vₚ × (Mf − Mₚ) / (Mₛ − Mf)
Mₛ must be greater than Mf. Mf must be greater than Mₚ.

Back Dilution — Add Diluent to Lower Concentration

V_diluent = V × (C₁ / C₂ − 1)

You overshot your target concentration. How much diluent (water, buffer) do you need to add to bring it back down?

C₁ — Current concentration

V — Current volume

C₂ — Target concentration

Diluent to add

V_diluent = V × (C₁ / C₂ − 1)
C₁ must be greater than C₂. Final volume = V + V_diluent.

Dilute to Exact Final Volume

V₁ = C₂ × V₂ / C₁

You have X mL at concentration C₁ and want exactly Y mL at concentration C₂. Tells you how much stock to use and how much diluent to add.

C₁ — Stock concentration

C₂ — Desired concentration

V₂ — Exact final volume needed

Pipetting instructions

V₁ = C₂ × V₂ / C₁ · V_diluent = V₂ − V₁
C₁ must be greater than or equal to C₂.

Mix Two Solutions of Different Concentrations

(M₁ × V₁) + (M₂ × V₂) = Mf × (V₁ + V₂)

Combine two solutions of the same solute at different concentrations. Calculates the resulting final concentration.

M₁ — Concentration of solution 1

V₁ — Volume of solution 1

M₂ — Concentration of solution 2

V₂ — Volume of solution 2

Final concentration (Mf)

Mf = (M₁ × V₁ + M₂ × V₂) / (V₁ + V₂)
Both solutions must contain the same solute. Units must be compatible.