Comprehensive Calculator Guide
To dilute a solution, use C1V1 = C2V2: the stock volume you need is the target concentration × final volume ÷ stock concentration. To make 500 mL at 2% from a 10% stock, take 100 mL of stock and make it up to 500 mL with water. Enter both concentrations and the final volume to get both amounts.
Why C1V1 = C2V2 works
Adding solvent does not change how much solute there is; it spreads it over more volume. Solute = concentration × volume before and after, so C1V1 = C2V2 and V1 = C2V2 ÷ C1. Any concentration unit works (%, mol/L, mg/L, ppm) as long as both concentrations use the same one. Adding solvent only dilutes, so the target cannot exceed the stock.
The solvent figure is V2 − V1, which assumes volumes add. That is close for dilute solutions, but some liquids such as alcohol and water shrink slightly when mixed, so in the lab measure V1 into a volumetric flask and fill to the mark.
Safety
Always add acid to water slowly, never water to acid: diluting releases heat and can make the mixture spit. Never mix household products, especially bleach with ammonia or acidic cleaners, which can release toxic gases. Dilute each with water only, with ventilation and gloves, and follow the label.
How to Use
- 01Enter the stock concentration.
- 02Enter the target concentration in the same unit.
- 03Enter the final volume in mL or L.
- 04Read the stock volume to measure and the approximate solvent to add.
Formula Used
C1 × V1 = C2 × V2 → V1 = C2 × V2 ÷ C1 | solvent ≈ V2 − V1Practical Examples
Example 1: 10% to 2%
For 500 mL: V1 = 2 × 500 ÷ 10 = 100 mL of stock plus about 400 mL of water.
Example 2: in the lab
1 M acid to 250 mL at 0.1 M: 25 mL of acid into a 250 mL flask, added to water, then filled to the mark.
Example 3: a cleaning product
A 5% product to 1 L at 0.1%: 20 mL of product made up to 1 litre with water.
Important Tips
- For very large dilutions, dilute in steps: three 1-in-10 steps give 1 in 1,000.
- Label diluted solutions with their concentration and date.
Common Mistakes to Avoid
- Using different concentration units for C1 and C2.
- Adding water to concentrated acid.
Frequently Asked Questions
- What is the dilution formula?
- C1V1 = C2V2: the amount of solute is the same before and after dilution.
- Do the units have to match?
- Yes: both concentrations in one unit, both volumes in one unit.
- Is 1:4 the same as 1:5?
- Conventions differ: 1:4 can mean one part stock to four parts water (a fivefold dilution) or one part in four total. Check what your instructions mean.
- Why can't the target be higher than the stock?
- Adding solvent only dilutes. Raising concentration needs more solute or evaporation.