Solution Dilution Calculator
Solve C₁V₁ = C₂V₂ for any unknown.
Enter 3 of the 4 values to get the dilution result.
Works for molarity, mg/mL, percent, or any other concentration unit.
The dilution equation is the most-used calculation in any wet lab. When you add solvent to a solution, you don’t change the amount of solute, only spread it across a larger volume. So the moles (or grams, or whatever) of solute before and after must be equal:
C₁V₁ = C₂V₂
C is concentration, V is volume. Subscripts 1 and 2 are before and after. The relationship works with any consistent concentration unit (molarity M, mg/mL, % w/v, ppm) and any consistent volume unit (mL, L, gallons) as long as both sides match.
Solving for each unknown
If you know three of the four values, the fourth is fixed:
| Solve for | Formula |
|---|---|
| Final concentration C₂ | C₂ = C₁ × V₁ / V₂ |
| Final volume V₂ | V₂ = C₁ × V₁ / C₂ |
| Stock concentration C₁ | C₁ = C₂ × V₂ / V₁ |
| Stock volume V₁ | V₁ = C₂ × V₂ / C₁ |
The calculator below figures out which one you’re solving for based on which field is left blank.
Worked example 1: making working HCl from concentrated stock
You have 100 mL of 6 M HCl and want to dilute it to 2 M. What final volume do you need?
V₂ = (6 × 100) / 2 = 300 mL
So you take the 100 mL of stock and add water to a final volume of 300 mL (that’s adding 200 mL of water).
Worked example 2: working backwards from final concentration
You diluted 25 mL of a stock solution to 500 mL and the final reading is 0.6 M. What was the stock concentration?
C₁ = (0.6 × 500) / 25 = 12 M
So the stock was 12 M, which matches concentrated HCl.
The safety rule: AAA (Always Add Acid)
When diluting concentrated acids (H₂SO₄, HCl, HNO₃), always add the acid to water slowly, never water to acid. The heat of dilution is large enough that water added to concentrated acid can flash to steam and splatter the acid back at you. The mnemonic is AAA: Always Add Acid. With gentle stirring and the water bath cool, the heat dissipates safely.
Why “add to volumetric mark” beats “add this much water”
Real volumes are not strictly additive. Mixing 100 mL of ethanol with 100 mL of water gives about 193 mL, not 200, because molecules pack more tightly in the mixture. For precise lab work, prepare solutions by diluting to a volumetric mark on a calibrated flask rather than measuring out water and adding it. The dilution equation assumes V₂ is the final total volume, not “V₁ plus the water you added.”
Serial dilution
For very dilute solutions, single-step dilution is impractical. Going from 1 M to 1 μM in one step would require 1,000,000-fold dilution in one flask. Instead, do serial dilution: three sequential 1:10 dilutions give 1:1,000; six give 1:1,000,000. Each step is easy to measure accurately.
Microbiology uses serial dilution constantly: starting with a culture too dense to count, dilute by 10× until colony counts fall below 300 per plate, then back-calculate the original concentration.
Common dilution patterns
| Pattern | Stock used | Diluent | Final |
|---|---|---|---|
| 1:10 | 1 part | 9 parts | 10 parts |
| 1:100 | 1 part | 99 parts | 100 parts (or 1:10 twice) |
| 1:2 | 1 part | 1 part | 2 parts |
| 1:5 | 1 part | 4 parts | 5 parts |
Notice the “diluent” column: a “1:10” dilution adds 9 parts of solvent, not 10. The total comes out to 10 parts. People mix this up constantly when reading protocols.
Where this calculation lives in real work
- Preparing buffer solutions from concentrated stock
- IV medication dose calculations (concentration in vial → dose in patient)
- Drink mixing (cocktail bartenders use C₁V₁ = C₂V₂ implicitly when adjusting alcohol content)
- Aquarium water chemistry (dilution to safe nitrate concentrations)
- Photographic developer concentrations (1:9 or 1:31 with water depending on the formulation)
- pH adjustment in water treatment, pool chemistry, and home brewing