100 mL at 10 mM from 100 mM
V₁ = 10 × 100 ÷ 100
Use 10 mL of stock and dilute to 100 mL total. The estimated diluent volume is 90 mL; the dilution factor is 10×.
Concentration and solution volume
Dilution Calculator
Find how much stock solution you need, or the final volume you can prepare, from the stock and target concentrations.
Calculate a dilution
Stock volume needed
Enter your values to see the result.
—
- Stock volume (V₁)
- —
- Final solution volume (V₂)
- —
- Estimated diluent volume (V₂ − V₁)
- —
- Dilution factor (C₁ ÷ C₂)
- —
Calculated in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Three worked examples
5 mL of 2 M stock to 250 mM
V₂ = 2,000 × 5 ÷ 250
First express 2 M as 2,000 mM. The final volume is 40 mL, with an estimated 35 mL of diluent and a factor of 8×.
50 mL at 100 mg/L from 2 mg/mL
V₁ = 100 × 50 ÷ 2,000
2 mg/mL equals 2,000 mg/L. You need 2.5 mL of stock diluted to 50 mL total. The estimated diluent is 47.5 mL.
Formula, units, and limits
Dilution conserves the amount of the same solute: C₁V₁ = C₂V₂. Subscripts 1 and 2 identify the stock portion and final solution. Therefore V₁ = C₂V₂/C₁ or V₂ = C₁V₁/C₂. The dilution factor is C₁/C₂ = V₂/V₁. See OpenStax — Molarity and Dilution.
Molar concentration is expressed in mol/L: 1 M = 1,000 mM = 1,000,000 µM. Mass concentration is expressed in g/L: 1 g/L = 1 mg/mL = 1,000 mg/L = 1,000 µg/mL. The two concentration bases cannot be mixed without the solute's molar mass. Volume conversion uses 1 L = 1,000 mL = 1,000,000 µL.
The diluent is assumed to contain none of the solute, with no reaction or loss of solute. The estimated diluent volume is V₂ − V₁ and assumes additive volumes; the conservation formula itself uses measured solution volumes. This tool does not calculate contraction, expansion, temperature effects, serial dilution steps, or mixing two solutions that both contain the solute.
All three numeric inputs must be positive. Target concentration can equal the stock concentration, in which case no dilution is needed. A higher target cannot be reached by adding diluent. A zero target cannot be reached with a positive stock portion and finite final volume in this model.
Inputs accept up to 64 characters, 15 integer digits, and 10 decimal places, including grouped numbers such as 1,000.50. Expressions, scientific notation, percent concentrations, and ppm are not accepted. Percent and ppm can use different mass or volume conventions, so this calculator does not guess their meaning.
Exact integer fractions retain the concentration ratio and all volume conversions. Only displayed values round, halfway away from zero. Trailing zeros are omitted; ≈ marks rounding. A positive volume displayed as zero receives a notice. Result-unit and precision changes reuse the original result without adding a history entry.
Common questions
Does a 10× dilution mean adding ten volumes of diluent?
No. A 10× factor means the final solution volume is ten times the stock portion. Under additive volumes, one volume of stock uses nine volumes of diluent.
Should I add 100 mL of diluent to make 100 mL of solution?
No. The final volume includes the stock portion. For the first example, use 10 mL of stock and bring the total solution to 100 mL.
Can I mix mg/mL and mM?
Not directly. Converting mass concentration to molar concentration requires the solute's molar mass. Choose two units on the same basis here.
Why is the estimated diluent volume zero?
The concentrations may be equal after conversion, meaning no dilution is needed. A very small positive difference may also round to zero; the result explanation distinguishes these cases.