# Dilution Calculator (C₁V₁ = C₂V₂)

Free dilution calculator using the C1V1 = C2V2 equation. Calculate initial concentration, initial volume, final concentration, or final volume.

## What this calculates

Use the dilution equation C₁V₁ = C₂V₂ to calculate any unknown variable in a dilution. This fundamental chemistry formula states that the product of concentration and volume remains constant when diluting a solution.

## Inputs

- **Solve For** — options: C₁ (Initial Concentration), V₁ (Initial Volume), C₂ (Final Concentration), V₂ (Final Volume) — Select which variable to calculate.
- **C₁ (Initial Concentration)** (M) — min 0 — Concentration of the stock/concentrated solution.
- **V₁ (Initial Volume)** (mL) — min 0 — Volume of stock solution to use.
- **C₂ (Final Concentration)** (M) — min 0 — Desired concentration after dilution.
- **V₂ (Final Volume)** (mL) — min 0 — Total volume of the diluted solution.

## Outputs

- **Result** — The calculated value.
- **Unit** — formatted as text — The unit of the result.
- **Formula** — formatted as text — The formula and calculation steps.
- **Solvent to Add** — formatted as text — Volume of solvent (water) to add.

## Details

The dilution equation is one of the most frequently used formulas in chemistry and biology labs. It is based on the principle that the number of moles of solute remains constant during dilution -- you are only adding solvent.

The Formula: C₁V₁ = C₂V₂

- C₁ = initial (stock) concentration

- V₁ = volume of stock solution used

- C₂ = final (diluted) concentration

- V₂ = final total volume

Rearranged Forms

- C₁ = (C₂ × V₂) / V₁

- V₁ = (C₂ × V₂) / C₁

- C₂ = (C₁ × V₁) / V₂

- V₂ = (C₁ × V₁) / C₂

Example

To make 500 mL of 0.1 M NaCl from a 1 M stock:
V₁ = (0.1 M × 500 mL) / 1 M = 50 mL
Take 50 mL of stock, add 450 mL of water.

## Frequently Asked Questions

**Q: What does C1V1 = C2V2 mean?**

A: C1V1 = C2V2 means that when you dilute a solution, the amount of solute stays the same. C1 and V1 are the concentration and volume before dilution; C2 and V2 are after. The product C×V represents moles of solute, which is conserved.

**Q: Do the units have to match?**

A: The concentration units must match on both sides (both M, both mg/mL, etc.), and the volume units must match on both sides (both mL, both L, etc.). You do not need to convert to specific units, as long as both sides use the same units.

**Q: What is a serial dilution?**

A: A serial dilution is a series of sequential dilutions, each using the previous diluted solution as the new stock. For example, a 1:10 serial dilution repeated 3 times gives dilutions of 1:10, 1:100, and 1:1000. C1V1=C2V2 applies to each step.

**Q: Can I use this formula for any concentration unit?**

A: Yes. The formula works with any concentration unit (M, mM, mg/mL, %, etc.) as long as C1 and C2 use the same unit. Similarly, V1 and V2 must use the same volume unit. The formula is unit-agnostic because it is based on conservation of solute.

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Source: https://vastcalc.com/calculators/chemistry/dilution
Category: Chemistry
Last updated: 2026-04-21