Dilution Calculator
Enter any three of C₁, V₁, C₂, V₂ to solve the fourth — and get exactly how much solvent to add. A live 3D beaker and charts show concentration dropping as volume grows.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any three values to solve for the fourth.
Live 3D dilution
Fix the solute (a stock C₁V₁), then grow the final volume — watch the liquid rise while the particles spread thinner and the concentration drops. Drag to orbit.
Dilution graphs
How dilution is calculated
The core idea in one line: pouring in solvent spreads the same amount of solute through a bigger volume, so the concentration falls in exact proportion to how much the volume grows.
Because the moles of solute are conserved, "moles before = moles after" becomes the dilution equation, which rearranges four ways:
C₁ = C₂V₂/V₁
V₁ = C₂V₂/C₁
C₂ = C₁V₁/V₂
V₂ = C₁V₁/C₂
The dilution factor ties it together: C₁/C₂ = V₂/V₁. A 10× dilution factor means the final volume is ten times the stock volume, and the concentration is one tenth. The formula is unit-agnostic — molarity, %, mg/mL, ppm all work, as long as each side is internally consistent.
Worked example 1 — diluting acid
Given: you have 50 mL of 6 M HCl. How much water makes it 1 M?
Worked example 2 — a serial dilution
Given: starting from 1 M, you do three successive 1:10 dilutions (take 1 part, add 9 parts solvent, three times). What is the final concentration?
Two ideas that trip students up
1. Same particles, more water
Both beakers hold the same number of solute particles. The right one just has more solvent, so they're spread thinner — lower concentration, identical moles.
2. Serial dilution multiplies
Each beaker takes a little of the one before and tops up with solvent. Three 1:10 steps stack to 1000× — the particle density visibly collapses along the row.
Making 1 L of solution from a 12 M stock
The more dilute the target, the less stock you need — stock volume is inversely proportional to the dilution factor.
| Target C₂M | Dilution factor | Stock V₁mL | Water addedmL |
|---|---|---|---|
| 6 | 2× | 500 | 500 |
| 1 | 12× | 83.3 | 916.7 |
| 0.1 ★ | 120× | 8.33 | 991.7 |
| 0.01 | 1200× | 0.83 | 999.2 |
★ Below ~1 mL of stock, measuring accurately by pipette gets hard — that's exactly when a serial dilution beats a single step. V₁ = C₂ × 1000 mL ÷ 12.
Where dilution actually matters
🧪 The lab bench
Concentrated stocks are cheaper to store and more stable, so almost every working solution is made by dilution. C₁V₁ = C₂V₂ is used dozens of times a day to turn stock into precise reagents.
💊 Medicine & pharmacy
IV drips, injectable drugs and reconstituted antibiotics are diluted to an exact concentration. Here a dilution error is a dosing error, so the calculation is checked and re-checked.
🔬 Calibration & microbiology
Serial dilutions build the ladder of known standards that calibrate instruments, and thin out bacterial cultures to countable colonies — accuracy at the bottom depends entirely on the dilution maths.
Common misconceptions
"V₂ is the amount of water you add."
V₂ is the total final volume, not the water added. The solvent to add is V₂ − V₁. Topping up to a mark on a volumetric flask gives V₂ directly.
"Diluting removes some solute."
It doesn't — the moles of solute are unchanged, just spread through more volume. That conservation is the whole reason C₁V₁ = C₂V₂ works.
"C₁ and C₂ can be in different units."
They must match. Mixing M on one side and mg/mL on the other breaks the equation. Convert first so both concentrations share a unit and both volumes share a unit.
"Add water to concentrated acid — it's faster."
Dangerous. Diluting acid is strongly exothermic; adding water to acid can make it boil and splash. Always add acid to water, slowly, with stirring.
Formula sources & further reading
The dilution relationship is standard general chemistry, traceable to:
- • OpenStax, Chemistry 2e — §3.4 "Molarity" (dilution of solutions; free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 4, Concentrations of Solutions (Dilution).
- • Zumdahl & Zumdahl, Chemistry — Chapter 4, Solution Stoichiometry.
C₁V₁ = C₂V₂ works with any consistent concentration and volume units. Results are rounded for display.
How to use this calculator
Enter three values
Fill any three of C₁, V₁, C₂, V₂ with consistent units — concentrations matching, volumes matching.
Get the fourth + steps
The missing value solves live, and for a dilution you get plain-English "take X, add Y solvent" instructions.
See it in the beaker
Use the sliders to watch concentration and particle density fall as the final volume grows.
Related tools
Frequently asked questions
What is the dilution equation?
C₁V₁ = C₂V₂. C₁ and V₁ are the initial concentration and volume, C₂ and V₂ the final ones. It holds because adding solvent changes the volume and concentration but not the number of moles of solute.
What units should I use?
Any consistent pair works — molarity with litres, mg/mL with mL, % with mL. The only rule is that both concentrations share one unit and both volumes share another; you never mix them within a side.
What is a serial dilution?
A stepwise dilution where each step reduces concentration by the same factor. Three 1:10 steps give 10 × 10 × 10 = 1000× total dilution — the standard way to reach very low, accurate concentrations for calibration and microbiology.
How do I prepare a dilution from a stock solution?
Rearrange to V₁ = C₂V₂ / C₁ to find the stock volume, then top up with solvent to V₂. For 100 mL of 0.1 M from a 1 M stock: V₁ = (0.1 × 100)/1 = 10 mL of stock, plus 90 mL of water.
Does diluting change the amount of solute?
No. Dilution adds solvent only; the moles of solute stay constant. That conservation of solute is exactly why C₁V₁ (moles before) equals C₂V₂ (moles after).
Which do I add to which — acid to water or water to acid?
Always add acid to water, slowly and while stirring. Diluting concentrated acid releases a lot of heat; adding water to acid can make it boil and spit dangerously.