What does C1V1 = C2V2 actually state?

That the amount of solute is conserved: concentration × volume before dilution equals concentration × volume after. Only solvent is added, so the product cannot change — everything a dilution calculation does follows from that one identity.

How much stock do I need for a target concentration?

V₁ = C₂·V₂ / C₁. For 50 mL of 10 mM from a 100 mM stock: 10 × 50 / 100 = 5 mL of stock, topped up with 45 mL of solvent. The calculator does this with your numbers and states the solvent explicitly.

What is a serial dilution and when is it better?

A chain of equal-factor dilutions — each step dilutes the previous one 1:10, say. It reaches very low concentrations that a single pipetting step cannot deliver accurately, and it is the standard construction for dose-response curves and plate assays.

Do the units need to be molar?

No. The identity is unit-agnostic: any concentration unit against any volume unit works, provided each pair is consistent. mg/mL with µL, percent with litres, X-fold buffer strengths — all fine, and the answer comes back in the same units.

What is a dilution factor?

The ratio C₁/C₂, equal to V₂/V₁ — a 1:10 dilution means the final mixture is ten times the stock volume drawn. Serial steps multiply: three 1:10 steps give a 1:1000 overall factor.

Dilution Calculator

Solve C₁V₁ = C₂V₂ for any variable and get a bench-ready recipe — stock to measure, solvent to add — plus a serial dilution planner.

The Dilution Calculator runs entirely in your browser. Concentrations and volumes are processed on your device and never uploaded.

Open the Molarity Calculator

About Dilution Calculator

Dilution Calculator is the C₁V₁ = C₂V₂ equation with the bench details handled. The identity says the amount of solute never changes — concentration times volume before equals concentration times volume after — and solving it for any one unknown is trivial algebra that is nonetheless fumbled daily. Pick what you are solving for (most often V₁, the stock volume to pipette), enter the other three values, and read the recipe: measure this much stock, add this much solvent, reach this final volume at this concentration. Units pass through unchanged, so molar with millilitres or µg/mL with µL both work as long as each pair stays consistent. The tool refuses impossible set-ups — a target above the stock concentration, a final volume smaller than the stock — instead of reporting negative solvent. The serial planner chains equal-factor steps, 1:10 or 1:2, the way plate assays are actually built.

Features

Solves for C₁, V₁, C₂ or V₂ — pick the unknown
Bench recipe: stock to measure and solvent to add
Dilution factor expressed as a 1:n ratio
Serial dilution planner with per-step concentrations
Molar, mass-per-volume, percent and X units supported
Refuses up-dilutions and negative solvent honestly
Sensible significant figures on every result
Everything computed on your device

How to use the Dilution Calculator

Choose which variable to solve for — usually V₁
Enter the other three values in consistent units
Read how much stock to measure and solvent to add
Use the serial planner for step-series like 1:10 ladders

Example

Input

Stock 100 mM · want 50 mL of 10 mM

Output

Measure 5 mL stock + 45 mL solvent — a 1:10 dilution

V₁ = C₂V₂/C₁ = 10×50/100 = 5 mL.

Common errors & troubleshooting

The calculator says the final concentration exceeds the stock. — Dilution can only reduce concentration — C₂ above C₁ needs evaporation or more solute, not water. Check for a units slip; mixing mM with µM is the usual culprit.
Negative solvent to add. — The requested final volume is smaller than the stock volume already implies. Increase V₂ or accept a smaller stock volume — the tool blocks the arithmetic that would hide this.
Results are off by exactly 1000×. — A unit mismatch between the two concentration fields (mM against µM) or the two volumes (mL against µL). The equation never converts units — both sides of each pair must match.
The serial ladder drifts from expected values at the far end. — Each step inherits the previous step's pipetting error, which compounds down the series. For critical low concentrations, prepare an intermediate stock and start a fresh ladder from it.

Frequently asked questions

What does C1V1 = C2V2 actually state?: That the amount of solute is conserved: concentration × volume before dilution equals concentration × volume after. Only solvent is added, so the product cannot change — everything a dilution calculation does follows from that one identity.
How much stock do I need for a target concentration?: V₁ = C₂·V₂ / C₁. For 50 mL of 10 mM from a 100 mM stock: 10 × 50 / 100 = 5 mL of stock, topped up with 45 mL of solvent. The calculator does this with your numbers and states the solvent explicitly.
What is a serial dilution and when is it better?: A chain of equal-factor dilutions — each step dilutes the previous one 1:10, say. It reaches very low concentrations that a single pipetting step cannot deliver accurately, and it is the standard construction for dose-response curves and plate assays.
Do the units need to be molar?: No. The identity is unit-agnostic: any concentration unit against any volume unit works, provided each pair is consistent. mg/mL with µL, percent with litres, X-fold buffer strengths — all fine, and the answer comes back in the same units.
What is a dilution factor?: The ratio C₁/C₂, equal to V₂/V₁ — a 1:10 dilution means the final mixture is ten times the stock volume drawn. Serial steps multiply: three 1:10 steps give a 1:1000 overall factor.

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