Dilution Calculator

How the Dilution Calculator works

Diluting a stock solution is one of the most common jobs in a lab, a kitchen or a garden shed. The amount of solute does not change when you add water, so the concentration falls in exact proportion to how much the volume grows. The concentration can be in any unit, molarity, percent or mg/L, as long as C₁ and C₂ use the same one.

How the dilution calculator works

The formula is C₁ × V₁ = C₂ × V₂, where C₁ and V₁ are the stock and the volume of it you take, and C₂ and V₂ are the diluted solution. Rearranged, V₁ = C₂ × V₂ ÷ C₁. The water to add is V₂ − V₁, and the dilution factor is C₁ ÷ C₂.

First example. To make 100 mL of 0.5 M acid from a 2 M stock, take V₁ = 0.5 × 100 ÷ 2 = 25 mL of stock and add 75 mL of water. That is a 4× dilution, one part stock to three parts water.

Second example. 10 mL of 12 M hydrochloric acid made up to 250 mL gives C₂ = 12 × 10 ÷ 250 = 0.48 M, a 25× dilution.

How many mL of stock do I need for a 1:10 dilution of 50 mL? One tenth of the final volume: 5 mL of stock plus 45 mL of water.

Making 100 mL of each concentration from a 1 M stock

Tips and pitfalls

• Same units on both sides. C₁ and C₂ must share a unit, and so must V₁ and V₂. The calculator uses one volume unit for both.
• Acid into water. When diluting strong acids, add the acid slowly to the water, never water to the acid, to avoid spitting.
• 1:10 can mean two things. In most labs it means 1 part in 10 total, but some recipes mean 1 part plus 10 parts. Check which, because the results differ by 10%.
• Serial dilutions for big factors. For a 1,000× dilution, three 10× steps are more accurate than measuring a tiny volume once.

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