Dilution Calculator

Solve C1V1 = C2V2 for any one concentration or volume. The calculator converts mixed units, shows the substitution, and reports the solvent volume when the inputs describe a dilution.

Quick reference for C1V1 = C2V2

You may mix the supported concentration units M, mM, µM, and nM, and the volume units L, mL, and µL. The calculator converts each input before applying the formula.

V2 is the final total volume, not the volume of water or solvent added. When V2 ≥ V1, the estimated solvent volume is V2 − V1.

What the dilution equation means

The equation is a solute-balance statement:

C1 × V1 = C2 × V2

For molar concentration, each side represents the same amount of solute in moles. You remove an aliquot of volume V1 from a stock at concentration C1, then bring it to a total volume V2. The resulting concentration is C2.

This calculation assumes that the amount of solute stays constant. It also assumes ideal volume additivity when it estimates V2 − V1 as the solvent to add. Real solutions can contract or expand on mixing. For accurate laboratory work, transfer the stock aliquot to a volumetric flask and dilute to the final-volume mark instead of measuring the solvent difference separately.

The formula is not suitable when the solute reacts, precipitates, evaporates, or changes chemical form during preparation. Concentration terms must also use the same basis. Do not mix molarity with mass percent unless you first convert them.

Worked example 1: prepare 100 mL of 1 mM solution

Suppose the stock concentration is 10 mM, the target concentration is 1 mM, and the final total volume is 100 mL. Solve for V1:

V1 = C2V2 / C1

V1 = (1 mM × 100 mL) / 10 mM = 10 mL

Take 10 mL of stock and dilute to a final total volume of 100 mL. Under the ideal-additivity estimate, the solvent amount is 100 − 10 = 90 mL. In a volumetric flask, the practical instruction is still "add solvent to the 100 mL mark."

Worked example 2: a mixed-unit microliter dilution

You have 100 µM stock, use 20 µL, and want 10 µM. Solve for the final volume:

V2 = C1V1 / C2

V2 = (100 µM × 20 µL) / 10 µM = 200 µL

The estimated solvent addition is 200 − 20 = 180 µL. If you choose mL for the result, the same final volume is 0.2 mL.

For calculations that start from a chemical formula rather than a prepared stock, first use the molar mass calculator. If a reaction equation is not balanced, check it with the chemical equation balancer before doing stoichiometry.

Common dilution mistakes

• Treating V2 as solvent added. It is the total final volume; solvent added is approximately V2 − V1.
• Entering the stock concentration as C2. C1 describes the solution before dilution.
• Mixing concentration bases such as molarity and percent without conversion.
• Forgetting that a target concentration above the starting concentration describes concentration, not dilution. The calculator warns instead of returning a negative solvent volume.
• Rounding V1 before the final step. Keep full precision, then round to the resolution of the pipette or flask.
• Assuming measured volumes always add exactly. For precision work, dilute to a final-volume mark.

Browse the chemistry calculators hub for the other formula and reaction tools in this set.

FAQ

What is the dilution formula?

The standard formula is C1V1 = C2V2. It states that the amount of solute before dilution equals the amount after dilution, provided no solute is lost or produced.

How much water should I add to make a dilution?

First calculate the final total volume V2. If V2 is at least V1, the ideal estimate for water or solvent is V2 − V1. For precise lab preparation, add solvent until the solution reaches the final-volume mark.

Can C1 and C2 use different units?

Yes. This calculator converts M, mM, µM, and nM internally. It also converts L, mL, and µL. A hand calculation should convert each concentration pair and volume pair to compatible units first.

What happens if C2 is greater than C1?

The inputs describe concentration rather than dilution. The equation can still solve the mathematical unknown, but adding solvent cannot raise concentration. The calculator labels this case and does not show a negative solvent amount.

When does C1V1 = C2V2 not apply?

Do not use it when the solute reacts, precipitates, evaporates, or otherwise changes amount. Its solvent estimate also assumes ideal volume additivity, which may not hold for real mixtures.

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