How to use the dilution calculator
Pick the quantity you need — most often the volume of stock to pipette — and enter the other three values. Every concentration and volume has its own unit, so you can dilute a 1 M stock to 50 mM in 250 mL, or 2 mL of a 0.1 mg/mL standard into 20 mL, without converting by hand. The result says how much stock to measure and how much diluent (water, buffer or solvent) makes up the rest, together with the dilution factor.
The two concentrations must be the same kind of unit: molar (M, mM, µM, nM), mass per volume (mg/mL and µg/mL — equal to g/L and mg/L), percent, or "×" for buffers sold as 10× or 50× concentrates. Going from mg/mL to molarity needs the molar mass; the molarity calculator does that step.
The dilution formula C1V1 = C2V2
Diluting adds solvent but not solute, so the amount of solute before and after is the same: C₁ × V₁ = C₂ × V₂. C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and total volume of the diluted solution. Rearranged: V₁ = C₂V₂ ÷ C₁, C₂ = C₁V₁ ÷ V₂, V₂ = C₁V₁ ÷ C₂ and C₁ = C₂V₂ ÷ V₁. The same equation is written M₁V₁ = M₂V₂ when the concentrations are molarities.
The dilution factor is C₁ ÷ C₂ = V₂ ÷ V₁. A tenfold dilution means one part stock in ten parts in total — written 1:10 in biology and medicine, which is 1 part stock plus 9 parts diluent. Cleaning concentrates and paints often write the ratio of concentrate to water instead; the calculator shows both, so check which one your instructions mean.
Worked examples
- Molar stock: 500 mL of 0.1 M from a 1 M stock needs V₁ = 0.1 × 500 ÷ 1 = 50 mL of stock plus 450 mL of water — a tenfold dilution.
- Different units: 1 L of 50 mM from 1 M: 50 mM = 0.05 M, so V₁ = 0.05 × 1000 ÷ 1 = 50 mL.
- Buffer concentrate: 100 mL of a 10× buffer made up to 1 L gives 1× working buffer.
- Percent: 100 mL of 70% ethanol diluted to 35% ends at 200 mL.
Serial dilutions
A serial dilution repeats the same step: each tube receives a fixed volume from the tube before and is topped up with diluent, so the concentration falls by the same factor every time. It is used for standard curves, antibody titrations and plate counts of bacteria, where one huge dilution would need impossibly small volumes. The table starts from the stock concentration C₁ and uses V₂ as the volume in each tube: for a tenfold series with 500 mL tubes, transfer 50 mL and add 450 mL of diluent. Six tenfold steps take a 1 M stock to 1 µM (1 : 1,000,000). Mix each tube well before the next transfer and use a fresh pipette tip each time.
Practical tips
- Fill up to the final volume rather than adding a calculated volume of water: volumes of ethanol and water, and of strong acids, are not exactly additive.
- Always add acid to water, never water to concentrated acid.
- Volumes below about 2 µL are hard to pipette accurately; make an intermediate dilution first or use a larger final volume.
- For medicines, follow the product information and your local protocols; this tool only checks the arithmetic.
Frequently asked questions
How do I calculate how much stock solution I need?
Multiply the final concentration by the final volume and divide by the stock concentration: V₁ = C₂ × V₂ ÷ C₁. For 500 mL of 0.1 M from a 1 M stock, that is 50 mL.
How much water do I add?
The final volume minus the stock volume, V₂ − V₁ — 450 mL in the example above. In practice, put the stock in a flask and fill up to the mark.
What does a 1:10 dilution mean?
One part of stock in ten parts in total (1 part stock plus 9 parts diluent), so the concentration drops to one tenth. Some product labels mean 1 part concentrate to 10 parts water instead — check the instructions.
Can I use C1V1 = C2V2 with percent or mg/mL?
Yes, as long as C₁ and C₂ use the same kind of unit. Mixing molar units with mg/mL needs the molar mass first.
How do I make a serial dilution?
Set the dilution factor and the number of tubes. Each tube gets V₂ ÷ factor from the tube before plus diluent up to V₂; the table lists the transfer, the diluent and the concentration in every tube.
Last updated: October 19, 2026