Dilution Calculator
Calculate the concentration or volume of a solution before and after dilution using the C₁V₁ = C₂V₂ formula. Find dilution factors, solvent volumes, and molarity conversions instantly.
Dilution Equation Solver
Solve for any missing variable in C₁V₁ = C₂V₂
Select the variable you want to calculate. The other three must be filled in.
Dilution Results
Calculated values and solvent requirements
Fill in three of the four variables and click Calculate Dilution to solve the equation.
Common Dilutions & Prefixes
Standard dilution ratios and molarity prefixes used in the laboratory.
| Dilution Ratio | Parts Sample | Parts Solvent | Total Parts |
|---|---|---|---|
| 1:2 | 1 | 1 | 2 |
| 1:10 | 1 | 9 | 10 |
| 1:100 | 1 | 99 | 100 |
| 1:1000 | 1 | 999 | 1000 |
| Prefix | Symbol | Factor |
|---|---|---|
| Molar | M | 10⁰ mol/L |
| Millimolar | mM | 10⁻³ mol/L |
| Micromolar | µM | 10⁻⁶ mol/L |
| Nanomolar | nM | 10⁻⁹ mol/L |
| Picomolar | pM | 10⁻¹² mol/L |
Dilution Calculator FAQ
Everything you need to know about solving dilution equations and preparing solutions.
The standard dilution formula is C₁V₁ = C₂V₂. In this equation, C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. You can use this formula to solve for any one of the four variables as long as you know the other three.
The dilution factor (DF) is the ratio of the initial volume to the final volume, or the initial concentration to the final concentration. It is calculated as DF = V₁ / V₂ or DF = C₂ / C₁. For example, if you dilute 1 mL of sample to a total volume of 10 mL, the dilution factor is 1/10 (often written as a 1:10 dilution).
A serial dilution is a stepwise dilution of a substance in solution. It involves taking a small volume of one dilution and transferring it to a new vessel containing solvent to create a new, more dilute solution. This process is repeated to achieve very high dilution factors accurately, commonly used in microbiology and biochemistry.
To prepare a 1:10 dilution, you mix 1 part of your stock solution with 9 parts of solvent. For example, if you need 10 mL of final solution, you would mix 1 mL of the stock with 9 mL of solvent. The total volume (V₂) is 10 mL, and the initial volume (V₁) is 1 mL.
The units must be consistent on both sides of the equation. This means C₁ and C₂ must be in the same concentration unit (e.g., both in mM), and V₁ and V₂ must be in the same volume unit (e.g., both in mL). This calculator automatically handles unit conversions if you choose different units for the initial and final values.
The amount of solvent to add is simply the final volume minus the initial volume: Solvent = V₂ – V₁. For example, if your initial volume is 5 mL and your final volume is 50 mL, you need to add 45 mL of solvent.
In most scientific contexts, a 1/10 dilution means 1 part sample in 10 parts TOTAL volume (1 part sample + 9 parts solvent). A 1:10 ratio can sometimes be interpreted as 1 part sample to 10 parts solvent (making 11 parts total). Always clarify the protocol, but standard laboratory practice usually equates 1:10 with a 1/10 dilution factor.
Yes, the C₁V₁ = C₂V₂ formula works for any concentration unit, including mass/volume percentages (% w/v), mg/mL, or ppm, as long as you use the same unit for both C₁ and C₂. This calculator supports generic units like ‘x’ (fold) and ‘%’ for these purposes.