Hong Life CalculatorsUnderstanding the dilution calculator — concept and principle
Diluting a concentrated stock to a working concentration is one of the most frequent tasks in a laboratory, a clinic, a darkroom or a garden shed. This calculator uses C₁V₁ = C₂V₂ to tell you how much stock to measure, how much diluent to add and what the dilution factor is.
How it is calculated
V₁ = C₂ × V₂ ÷ C₁
- C₁: stock concentration. C₂: final concentration. Both in the same unit (M, %, mg/mL, anything).
- V₂: final total volume in mL.
- Diluent to add = V₂ − V₁.
- Dilution factor = C₁ ÷ C₂.
The principle
Adding solvent changes the volume but not the amount of solute. The amount of solute in the portion of stock you take is C₁ × V₁, and after dilution the same amount is spread through V₂, so C₁V₁ = C₂V₂. Because the concentration units appear on both sides, they cancel; you only need C₁ and C₂ in the same unit. The diluent volume is found by simple subtraction, which assumes volumes are additive.
Worked example
Defaults: C₁ = 10, C₂ = 0.5, V₂ = 100 mL.
- V₁ = 0.5 × 100 ÷ 10 = 5 mL of stock.
- Diluent = 100 − 5 = 95 mL.
- Dilution factor = 10 ÷ 0.5 = 20 (a 1:20 dilution).
| Stock concentration C1 | Stock volume V1 (mL) |
|---|---|
| 2.5 | 20 |
| 5 | 10 |
| 7.5 | 6.666666667 |
| 10 | 5 |
| 12.5 | 4 |
| 15 | 3.333333333 |
| 20 | 2.5 |
How to read the result
A dilution factor of 20 means the final solution is one twentieth as concentrated as the stock: 1 part stock in 20 parts total, which is 1 part stock plus 19 parts diluent. If V₁ comes out very small (below about 1 mL with ordinary pipettes), measuring error grows; consider a two-step or serial dilution instead. If C₂ is larger than C₁ the result is impossible, since dilution can only lower the concentration.
Common mistakes
- Using different units for C₁ and C₂, such as M and mM.
- Adding V₂ of diluent to V₁ of stock, which overshoots the final volume.
- Confusing "1:20" (1 part in 20 total) with "1 + 20" (1 part plus 20 parts, total 21), which some fields use.
- Ignoring volume contraction when mixing concentrated acids or ethanol with water.
Frequently asked questions
Can I use percentages in this formula?
Yes, as long as both concentrations are the same kind of percentage (both % w/v or both % v/v).
How do I dilute 1:100 with a small final volume?
For 10 mL, use 0.1 mL of stock and 9.9 mL of diluent, or do two 1:10 steps for better accuracy.
What is the difference between dilution factor and dilution ratio?
The factor is total volume ÷ stock volume (20 here); a ratio is often written as stock : diluent (1 : 19). Check which convention a protocol uses.
Sources: Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman · Skoog, D. A., West, D. M., Holler, F. J., Crouch, S. R., Fundamentals of Analytical Chemistry, Cengage