Solution Dilution Calculator
Solve the conservation relationship C₁V₁ = C₂V₂, convert compatible units, and export the current calculation to a validated Excel workbook.
Inputs
Live results
Calculation breakdown
| Quantity | Entered / calculated value | Canonical value | Role in equation |
|---|---|---|---|
| Stock concentration (C₁) | 2 M | 2 base units | C₁ × V₁ |
| Stock volume (V₁) | 25 mL | 25 mL | C₁ × V₁ |
| Final concentration (C₂) | 0.5 M | 0.5 base units | C₂ × V₂ |
| Final volume (V₂) | 100 mL | 100 mL | C₂ × V₂ |
How to use the solution dilution calculator
What this calculator does
This calculator solves the standard dilution identity C₁V₁ = C₂V₂. It treats the amount of dissolved solute as unchanged while solvent is added, so the product of concentration and volume before dilution equals the product afterward. It is useful for planning a single-step laboratory dilution, checking a preparation worksheet, scaling a recipe for a standard solution, or verifying that a target concentration and final volume are consistent with an available stock. It does not account for chemical reaction, evaporation, incomplete transfer, volume contraction on mixing, density changes, or uncertainty in glassware.
When to use it
Use it when preparing a working solution from a stronger stock, converting a protocol to a different batch size, checking how much concentrate is needed for a target volume, or finding the final concentration after adding solvent. The relationship is explained in the LibreTexts guide to solution dilution.
How to calculate
- The calculator opens with a complete demonstration: 2 M stock, 25 mL stock volume, and 100 mL final volume. The calculated final concentration is 0.5 M, and the example workbook is immediately available.
- Choose Solve for. The selected field becomes read-only, while the other three quantities become inputs.
- Enter positive decimal values. The parser accepts U.S.-style decimal points and optional thousands separators; scientific notation and decimal commas are rejected to avoid silent reinterpretation.
- Select compatible concentration units and volume units. M, mM, and µM form one concentration family; g/L and mg/mL form another equivalent mass-per-volume family; percent is only compatible with percent on the same stated basis. Volumes are converted through millilitres.
- Read the primary result, dilution factor, solvent volume, conservation check, and the calculation table. Choose Download Excel to export the current validated model.
- Reset clears all four values and restores neutral unit selections. The export button is disabled until three complete valid inputs are entered again.
Input guide
Solve for is required and determines which one of the four variables is calculated. Stock concentration (C₁) is the concentration before adding solvent; enter a positive decimal such as 2 and select its unit. Stock volume (V₁) is the aliquot taken from the stock, such as 25 mL. Final concentration (C₂) is the target or measured concentration after dilution, such as 0.5 M. Final volume (V₂) is the total solution volume after dilution, such as 100 mL – not the volume of solvent alone. A common mistake is entering 75 mL as V₂ in this example; 75 mL is the solvent added, while the final volume is 25 + 75 = 100 mL. All three entered quantities are required, finite, and greater than zero. For an ordinary dilution, V₂ should be at least V₁ and C₂ should not exceed C₁; the calculator flags a concentration increase or negative solvent addition as inconsistent with dilution.
Output guide
The primary result is the selected unknown, shown in its chosen display unit. Dilution factor is V₂/V₁, equivalently C₁/C₂, so 4× means one part stock is brought to four parts total volume. Solvent to add is V₂ – V₁ in the final-volume unit; zero means no dilution and a negative value indicates the inputs describe concentration rather than dilution. Conservation check displays both sides of C₁V₁ = C₂V₂ in compatible canonical units. The table lists each variable, its display value, canonical value, and equation role. These are exact algebraic identities for the entered idealized model, not a guarantee of experimental accuracy.
Worked example
For the startup example, C₁ = 2 M, V₁ = 25 mL, and V₂ = 100 mL. Rearranging gives C₂ = C₁V₁/V₂ = (2 × 25)/100 = 0.5 M. The dilution factor is 100/25 = 4, and the solvent volume is 100 – 25 = 75 mL. Both sides of the conservation equation equal 50 M·mL. In practical preparation, transfer 25 mL of stock to suitable volumetric glassware, then add solvent until the total volume reaches 100 mL and mix thoroughly. The RMIT concentration and dilution lesson explains why the amount of solute remains constant during this ideal calculation.
Formula, units, and interpretation
C₁V₁ = C₂V₂
The equation works because concentration multiplied by volume represents an amount of solute on a consistent basis. Unit conversion is therefore allowed only within compatible families. Molar units can be converted by powers of one thousand, and volume units can be converted through litres or millilitres. Mass concentration can be used in g/L or mg/mL because those two units are numerically equivalent. Converting between molar concentration and mass concentration requires the solute's molar mass, which is intentionally outside this calculator's scope.
For good laboratory practice, use calibrated volumetric glassware, read the meniscus correctly, and consider measurement uncertainty. The NIST guidance on SI volume units provides authoritative context for litre-based measurements. A calculated dilution is only as reliable as the stock concentration and the delivered volumes.
Common mistakes and limits
- Using solvent volume as final volume.
- Mixing incompatible concentration bases, such as mol/L with g/L, without molar mass.
- Assuming volumes are always perfectly additive for every solvent system.
- Ignoring transfer losses, temperature effects, or stock degradation.
- Using the simple equation for a chemical reaction, serial dilution chain, or continuously fed process.
For safety-sensitive work, follow the relevant laboratory procedure and chemical safety documentation. The OSHA laboratory safety resources summarize general controls for laboratory work.