Dilution CalculatorC1V1 = C2V2 solver with diluent volume and dilution factor
Find how much stock to measure, how much diluent to add, or what strength you will end up with. Works in molar, mg/mL, percent and 10X-style units.
By Manzoor Ahmad, web development expert · Updated How do you calculate a dilution?
Use C1V1 = C2V2 and solve for the unknown. To find stock volume, V1 = C2 × V2 ÷ C1. Example: 250 mL of 0.9% saline from 23.4% concentrate needs 0.9 × 250 ÷ 23.4 = 9.6 mL of concentrate, made up to 250 mL with 240.4 mL of diluent. The dilution factor is C1 ÷ C2 = 26.
Stock (start)
Final (target)
The dilution formula and its four rearrangements
Adding solvent spreads the same amount of solute through a larger volume. Because the moles (or grams) of solute stay constant, concentration × volume is equal before and after: C₁V₁ = C₂V₂.
Two values fall out of every dilution: the diluent volume (V₂ − V₁) and the dilution factor (C₁ ÷ C₂, equal to V₂ ÷ V₁).
How to use the dilution calculator
- Choose which value you want to find. That field greys out.
- Enter the other three values with their units. Both concentrations must be the same type, for example M and mM, or % and mg/mL.
- Read the answer, the diluent volume, the dilution factor and the mixing ratio.
- Check the warning panel. If the stock volume is too small to measure accurately, plan an intermediate step.
Worked examples
1. Normal saline from concentrated sodium chloride (pharmacy)
This is the calculator’s default. You need 250 mL of 0.9% w/v sodium chloride, and the stock is 23.4% w/v concentrate.
- V₁ = (0.9 × 250 mL) ÷ 23.4 = 9.615 mL → measure 9.6 mL.
- Diluent = 250 − 9.6 = 240.4 mL (in practice, fill to 250 mL).
- Dilution factor = 23.4 ÷ 0.9 = 26, a 1:26 dilution.
Concentrated sodium chloride is a high-alert medicine. In clinical settings this preparation is done under a verified protocol with independent double checks. Treat this example as arithmetic practice.
2. 50X TAE buffer to 1X (molecular biology)
For 1 L of 1X from 50X stock: V₁ = (1 × 1000 mL) ÷ 50 = 20 mL of stock plus 980 mL of water. Select the “X (fold)” unit for both concentrations.
3. Molar stock to working solution (chemistry)
From 2.0 M HCl, 100 mL of 50 mM is: V₁ = (0.050 M × 100 mL) ÷ 2.0 M = 2.5 mL. The calculator converts mM to M automatically. Always add acid to water, not water to acid.
Dilution factor reference for 100 mL of final solution
| Dilution | Dilution factor | Stock volume | Diluent volume | Final strength |
|---|---|---|---|---|
| 1:2 | 2 | 50 mL | 50 mL | 50% of stock |
| 1:5 | 5 | 20 mL | 80 mL | 20% of stock |
| 1:10 | 10 | 10 mL | 90 mL | 10% of stock |
| 1:20 | 20 | 5 mL | 95 mL | 5% of stock |
| 1:50 | 50 | 2 mL | 98 mL | 2% of stock |
| 1:100 | 100 | 1 mL | 99 mL | 1% of stock |
| 1:1000 | 1,000 | 0.1 mL (100 µL) | 99.9 mL | 0.1% of stock |
Beyond about 1:100 in a single step, measuring errors grow. For 1:1000 and above, a serial dilution (for example three 1:10 steps) is usually more accurate.
Dilution mistakes that cause wrong answers
- Mixing concentration types. 10 mM and 1 mg/mL cannot go into the same equation unless you convert using molar mass.
- Adding V₂ of diluent. V₂ is the final total volume. The diluent is V₂ − V₁.
- Mismatched volume units. The calculator converts them, but by hand, mL on one side and L on the other gives errors of 1,000×.
- Reading 1:10 two ways. Confirm whether your protocol means 1 part in 10 total, or 1 part plus 10 parts.
Dilution calculator FAQs
The dilution formula is C1V1 = C2V2, where C1 and V1 are the concentration and volume of the stock, and C2 and V2 are the concentration and volume of the final diluted solution. It works because the amount of solute does not change when you add solvent.
Rearrange to V1 = (C2 × V2) ÷ C1. To make 250 mL of 0.9% saline from 23.4% concentrate, V1 = (0.9 × 250) ÷ 23.4 = 9.6 mL of stock.
Diluent volume = final volume − stock volume (V2 − V1). In the saline example that is 250 − 9.6 = 240.4 mL. For best accuracy, fill to the final volume mark rather than measuring the diluent separately.
The dilution factor is the stock concentration divided by the final concentration (C1 ÷ C2), which also equals V2 ÷ V1. A dilution factor of 10 means the solution is ten times weaker, also written as 1:10.
In most lab usage a 1:10 dilution means 1 part stock in 10 parts total, for example 1 mL stock plus 9 mL diluent. Some older texts mean 1 part stock plus 10 parts diluent, so confirm which convention your protocol uses.
They must measure the same kind of concentration. You can mix mM and M, or mg/mL and % w/v, because the calculator converts within each family. You cannot directly compare molar and mass units without the molar mass.
Use V1 = V2 ÷ 10. For 1 L of 1X buffer from a 10X stock, use 100 mL of stock and make up to 1 L. For a 50X stock, use 20 mL per liter.
Dilution can only lower concentration. If the target is stronger than the stock, you need a more concentrated stock or a different method, such as dissolving more solute.
Yes, as long as both concentrations are in the same type of percent, such as % w/v for both. This is how pharmacists calculate dilutions of concentrates in compounding.
Volumes under about 10 µL are hard to pipette accurately. Make an intermediate dilution first, then dilute that, or use the serial dilution calculator to plan several steps.
Yes. M1V1 = M2V2 is the same equation written with molarity (M) as the concentration unit. The calculator accepts M, mM, µM and nM.
Not always. Some liquids, such as ethanol and water, contract slightly when mixed. That is why filling to a volumetric mark gives a more accurate final volume than adding measured volumes.
Sources
This dilution calculator is for education and planning. Clinical, compounding and safety-critical dilutions must follow validated procedures and an independent double check.