Dilution calculator (C₁V₁ = C₂V₂ and 1:N ratios)
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Dilutions follow C₁V₁ = C₂V₂: stock concentration times stock volume equals final concentration times final volume. To find how much stock to use, V₁ = C₂V₂ / C₁. Making 100 ml of 1× buffer from a 10× stock takes 10 ml of stock plus 90 ml of diluent.
Result
C₁V₁ = C₂V₂. Units cancel: use any concentration unit and any volume unit, as long as each pair matches.
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What it looks like
Formula
C₁V₁ = C₂V₂ → V₁ = C₂ × V₂ / C₁
Source: Conservation of solute; Promega BioMath dilution calculator
Worked example
Given: Make 100 ml of 1× TAE from a 10× stock
- 1.V₁ = C₂ × V₂ / C₁ = 1 × 100 / 10 = 10 ml of stock.
- 2.Diluent: 100 − 10 = 90 ml of water.
10 ml of 10× stock + 90 ml water
How the calculation flows
Units & constants
| Solves for | Any one of C₁, V₁, C₂, V₂ |
|---|---|
| Units | Any, as long as both concentrations match and both volumes match |
| Also reports | Diluent volume to add (V₂ − V₁) when solving for V₁ |
| Limits | Assumes volumes are additive: true for dilute aqueous solutions |
| Price | Free |
How much stock for a 1:200 dilution? Ratio dilution chart
| Dilution | Stock, 1 ml final | Diluent, 1 ml final | Stock, 10 ml final | Diluent, 10 ml final |
|---|---|---|---|---|
| 1:2 | 500 µl | 500 µl | 5 ml | 5 ml |
| 1:5 | 200 µl | 800 µl | 2 ml | 8 ml |
| 1:10 (10X to 1X) | 100 µl | 900 µl | 1 ml | 9 ml |
| 1:20 | 50 µl | 950 µl | 500 µl | 9.5 ml |
| 1:50 | 20 µl | 980 µl | 200 µl | 9.8 ml |
| 1:100 | 10 µl | 990 µl | 100 µl | 9.9 ml |
| 1:200 | 5 µl | 995 µl | 50 µl | 9.95 ml |
| 1:500 | 2 µl | 998 µl | 20 µl | 9.98 ml |
| 1:1,000 | 1 µl | 999 µl | 10 µl | 9.99 ml |
Dilution-factor convention: 1:N means 1 part stock in N parts final volume, so stock = final volume / N. Some kits write ratios as stock to diluent (1:199 for the same dilution); check which your protocol means.
How much stock do I need: the only equation to remember
C₁V₁ = C₂V₂ works because dilution changes volume, not the amount of solute: moles before equals moles after. Rearranged, V₁ = C₂V₂/C₁ answers the everyday question 'how much of my stock goes into this tube?'. The same relation solved for C₂ answers 'what did my concentration become after adding X to Y?'.
What units can you use?
Any, so long as they cancel.
- Concentrations: M, mM, µM, mg/ml, ng/µl, ×-fold, %. Both sides must use the same one.
- Volumes: L, ml, µl. Both sides must use the same one.
- Fold-stocks (10×, 50×) are just concentrations in disguise: 10× → 1× is C₁ = 10, C₂ = 1.
When is a single dilution not enough?
When the ratio exceeds what you can pipette accurately, going from 1 M to 1 µM in one step means pipetting 0.1 µl into 100 ml territory. Chain smaller steps instead (e.g. three 1:100 dilutions), keeping every pipetted volume above ~2 µl. A serial-dilution planner for exactly this is on the roadmap and linked from here when it ships.
Frequently asked questions
Add 1 part stock to 199 parts diluent: 5 µl of stock into 995 µl gives 1 ml at 1:200, and 50 µl into 9.95 ml gives 10 ml. This is C₁V₁ = C₂V₂ with V₁ = V₂ / 200.
A 10X to 1X dilution is 1:10: one part buffer in ten parts final volume. For 50 ml of 1X, mix 5 ml of 10X buffer with 45 ml of water; for 1 L, 100 ml with 900 ml.
Yes. Percent is a concentration like any other, so diluting 70% ethanol to 50% follows the same relation: V₁ = 50 × V₂ / 70. Both concentrations just have to be the same kind of percent (w/v or v/v).
Solve for C₂: C₂ = C₁V₁ / V₂, where V₂ is the total volume after mixing. Adding 5 µl of 10 mM stock to 95 µl of buffer gives 10 × 5 / 100 = 0.5 mM.
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