Solution Dilution Calculator
A free solution dilution calculator for the most common bench task: you have a concentrated stock and want to dilute it to a lower target concentration. Enter C₁, C₂ and the final volume to get the stock volume to take and the solvent to add.
Enter the stock concentration, the final concentration you want, and the final volume to find the stock volume to take.
How to dilute a stock solution
Diluting a stock means lowering its concentration by adding more solvent while the amount of solute stays the same. Because the solute is conserved, the dilution equation holds:
Here C₁ is your stock concentration, C₂ is the final concentration you want, and V₂ is the final volume you need to make. The unknown is V₁, the volume of stock to measure out. Rearranging for V₁ gives:
Once you know V₁, the solvent to add is just the final volume minus the stock volume: solvent = V₂ − V₁. Measure V₁ of stock, then top up with solvent until you reach V₂.
Worked example
Suppose you have a 10 M stock and need 50 mL of a 1 M working solution. Set C₁ = 10 M, C₂ = 1 M and V₂ = 50 mL: V₁ = (1 × 50) ÷ 10 = 5 mL of stock. The solvent to add is 50 − 5 = 45 mL. So you measure 5 mL of the 10 M stock and add 45 mL of solvent to reach 50 mL of 1 M solution.
Related tools
Need to solve for a different unknown instead of the stock volume? Use the home dilution calculator, which solves C₁V₁ = C₂V₂ for any of the four values. To work out a stock concentration from a mass and molecular weight first, use the molarity calculator.
Frequently asked questions
›How do I use the solution dilution calculator?
Enter the concentration of your stock solution (C₁), the final concentration you want after diluting (C₂), and the final volume you need (V₂). The calculator returns V₁ — the volume of stock to measure out — and tells you how much solvent to add to reach the final volume. C₁ and C₂ share one concentration unit, so they cancel in the ratio.
›What is the solution dilution formula?
It is the rearranged dilution equation C₁V₁ = C₂V₂, solved for the stock volume: V₁ = (C₂ × V₂) ÷ C₁. Once you know V₁, the amount of solvent to add is simply the final volume minus the stock volume, V₂ − V₁.
›Why can I not dilute to a higher concentration?
Adding solvent only ever lowers concentration, so the final concentration C₂ must be less than or equal to the stock concentration C₁. If you ask for a C₂ greater than C₁, diluting cannot get you there — you would need a more concentrated stock or a different solute mass instead.
›Do C₁ and C₂ need the same unit?
Yes. Because the formula is a ratio (C₂ ÷ C₁), the stock and final concentrations must use the same unit — M, mM, µM, mg/mL or % — and the unit then cancels out. The resulting stock volume V₁ comes out in whatever volume unit you chose for V₂.
Related calculators
Solve C₁V₁ = C₂V₂ for any unknown — stock concentration, volume, or final concentration.
Find molarity from mass and molecular weight, or the mass needed for a target molarity.
Convert between moles, volume, and molar concentration (mol/L) in any direction.
Turn a 1:N ratio into exact stock + solvent volumes for any final amount.
Convert mg/mL to molarity (and back) using molecular weight — both directions.
Parts per million ⇆ mg/L ⇆ percent, plus the mass of solute for a target ppm.