Chemistry · 5 min read
How to Use C1V1 = C2V2
Dilution conserves moles of solute — solve V2 from C1, V1, and C2
A dilution keeps the amount of solute fixed while the solution volume changes. That conservation is C1 V1 = C2 V2. This tutorial walks through the identity, a C1 = 1, V1 = 50, C2 = 0.1 worked example matching the Dilution Calculator, and beakers that rebalance as you change concentration or volume.
Written by the My Calculator Stack editorial team. About our methods
C1V1 = C2V2 conserves moles of solute. C1 and C2 must share a concentration unit, V1 and V2 a volume unit, and C2 must be nonzero. This is study arithmetic, not a lab protocol.
1.What the dilution identity is
The amount of solute is concentration times volume. If you add solvent and do not add or remove solute, that amount stays the same: C1 V1 = C2 V2. C1 and V1 are the stock; C2 and V2 are the diluted mixture. When C2 is smaller than C1, V2 is larger than V1 — a dilution. The same algebra also describes concentrating if C2 > C1.
2.The formula
Solve for the unknown you need. The Dilution Calculator reports V2 = (C1 V1) / C2. C2 must be nonzero. Matching units matter: mol/L with mol/L, mL with mL. The identity does not track mixing heat, non-additive volumes, or how you physically transfer the stock.
\[ C_1V_1=C_2V_2 \]
3.Worked example
Take C1 = 1, V1 = 50, and C2 = 0.1 — the same defaults as the Dilution Calculator. Solute amount is 1 × 50 = 50 (in C×V units). Then V2 = 50 / 0.1 = 500. A tenfold drop in concentration needs a tenfold rise in volume. Check: 0.1 × 500 = 50, same moles.
\[ V_2=\frac{(1)(50)}{0.1}=500 \]
4.Beaker playground
Move stock concentration, stock volume, and target concentration. The beakers rebalance so C1 V1 stays equal to C2 V2: fill height tracks volume, and color intensity tracks concentration. This is a teaching widget — no favorites, no full calculator chrome. Open the Dilution Calculator when you want the standalone tool.
Inline playground
Final volume V2
500
V2 = (1 × 50) / 0.1 = 500
Stock
C1=1 · V1=50
C1V1 = C2V2
Diluted
C2=0.1 · V2=500
Teaching aid only — C2 must be nonzero. Matching concentration and volume units are assumed.
Open the full Dilution calculator →5.Open the full calculator
The Dilution Calculator uses the same C1 V1 = C2 V2 identity and the same 1 / 50 / 0.1 example, with How it works and FAQ on one page. Browse other chemistry calculators if you need moles or related stoichiometry next.
Try it yourself
Open the related calculator and put these formulas to work.