C1V1 = C2V2 Calculator for Dilution Percent

The C1V1 = C2V2 calculator finds the volume of a starting solution needed to prepare a target concentration by dilution. Enter the starting concentration (C1), its volume (V1), the target concentration (C2), and the final volume (V2); the calculator returns the missing volume or concentration and expresses the result as a percent when the concentration units are percentages.

Formula

The dilution equation is C1V1 = C2V2. It states that the amount of solute before dilution equals the amount of solute in the final solution, assuming no solute is lost or added during the dilution.

• C1 is the starting concentration, entered here as a percent.
• V1 is the volume of starting solution, in millilitres.
• C2 is the target concentration, entered in the same percent units as C1.
• V2 is the final total solution volume, in millilitres.

The calculator shows three useful rearrangements: V1 = C2V2/C1, C2 = C1V1/V2, and V2 = C1V1/C2. Its first result is the starting volume required for the requested target concentration and final volume. The other results show the concentration or final volume implied by the entered values. Use a percent symbol consistently for both concentrations; because the ratio C2/C1 is dimensionless, the percent values cancel.

Worked Example

With the default inputs, C1 = 10%, V1 = 25 mL, C2 = 2%, and V2 = 125 mL.

1. Starting volume required: V1 = C2V2/C1 = (2% × 125 mL) / 10% = 25.00 mL.
2. Target concentration implied by the entered volumes: C2 = C1V1/V2 = (10% × 25 mL) / 125 mL = 2.00%.
3. Final volume implied by the entered starting volume and target: V2 = C1V1/C2 = (10% × 25 mL) / 2% = 125.00 mL.

The matching values show that the default inputs are internally consistent: 25 mL of a 10% solution contains the same solute amount as 125 mL of a 2% solution, under the assumptions of the equation.

Assumptions

• The starting and target concentrations use the same definition of percent and the same basis, such as mass/volume or volume/volume.
• The solute amount is conserved during dilution; there is no reaction, evaporation, precipitation, or transfer loss.
• V2 means the final total solution volume, not the volume of solvent to add.
• The calculation is arithmetic for study and lab planning, not a preparation procedure. For bench work, follow your lab method, the safety data sheet (SDS), and your supervisor.

What “Percent” Means in C1V1 = C2V2

Percent is not a single concentration convention. A solution labeled 10% may mean 10 g of solute per 100 mL of solution (% w/v), 10 mL per 100 mL (% v/v), or 10 g per 100 g (% w/w). The dilution equation can be used with these forms when the starting and target concentrations use the same basis. The calculator’s percent symbol does not identify which basis you mean, so keep the source label or method with your result.

For example, a 10% w/v stock and a 2% w/v target can be used together in the equation. But mixing a 10% w/v value with a 2% w/w value is not valid as entered: the units describe different quantities, and conversion may require density or other substance-specific information. If your values are expressed in mol/L, mg/mL, or another concentration unit instead, you can still use C1V1 = C2V2, provided both concentration entries use the same unit. Do not enter one value as a decimal fraction, such as 0.10, and the other as 10, unless you first convert them to a consistent form.

How to Use the Calculator

1. Identify the starting concentration and target concentration, including the percent basis or concentration unit.
2. Enter the desired final total volume. This is the volume the finished solution is meant to occupy.
3. Read the first result as the volume of starting solution needed. The other outputs are cross-checks calculated from the input values.
4. Check that the result is physically sensible. For a dilution to a lower concentration, the target should be below the starting concentration, and the starting-solution volume should be below the final volume.

If you already know the starting volume and final volume, the calculator’s second output gives the resulting concentration. If you know the starting and target concentrations plus the amount of stock available, its third output gives the final volume that amount can produce.

Common Mistakes and Limits

• Adding the wrong volume: V2 is the final solution volume. If the calculation says to use 25 mL of stock for a final volume of 125 mL, it does not mean to add 125 mL of solvent to the stock.
• Using different percent bases: % w/v, % v/v, and % w/w are not interchangeable without appropriate conversions.
• Mixing units: Concentrations must be expressed on the same basis, and volume units should match. Convert litres to millilitres or vice versa before comparing volumes.
• Rounding too early: Keep extra digits during calculations and round the reported value to a practical precision appropriate to the measurements and method.
• Assuming dilution changes only volume: The equation does not account for chemical reactions, concentration-dependent volume changes, or material lost during transfer.

The equation is a conservation relationship, not a guarantee that a real mixture behaves ideally. In particular, mixing liquids can change their total volume, and some solutes may react or come out of solution. For rigorous work, use the concentration definition and preparation method relevant to the substance and application.

Frequently Asked Questions

How do I calculate C1V1 = C2V2 as a percent?
Put C1 and C2 in the same percent format, then rearrange the equation for the unknown. For the starting volume, use V1 = C2V2/C1. The percent units cancel in the ratio.

Does C1V1 = C2V2 tell me how much water to add?
It gives the volume of stock and the target final volume. The difference between those volumes can be a useful nominal solvent amount, but the equation defines V2 as the final total volume. Add solvent to reach the specified final volume rather than assuming volumes always add exactly.

Can I use C1V1 = C2V2 for molarity?
Yes, when both concentrations are in the same units, such as mol/L, and the volume units are consistent. The equation is commonly used for dilution calculations because the amount of solute is treated as conserved.

What if my target concentration is higher than C1?
That is not a dilution. The calculated starting volume may exceed the desired final volume, indicating that the requested result cannot be obtained by adding solvent to the stated stock. A more concentrated source or a different preparation calculation is needed.

Are percent concentrations always interchangeable?
No. Percent may mean mass per volume, volume per volume, or mass per mass. Use matching definitions for C1 and C2; conversion between bases can require density and other information.

Related

• Serial Dilution Calculator: Molar Concentration After n Steps
• Dilution Formula Calculator: C1V1 = C2V2 for Molarity
• Dilution Factor Calculator: Final Molarity From Volumes

in c1 | Starting concentration C1 | % | 10 | 0
in v1 | Starting volume V1 | mL | 25 | 0
in c2 | Target concentration C2 | % | 2 | 0
in v2 | Final volume V2 | mL | 125 | 0
out p | Starting volume required V1 | mL | v2 * c2 / c1 | 2
out cp | Target concentration | % | c1 * v1 / v2 | 2
out vp | Final volume | mL | c1 * v1 / c2 | 2