Solution Dilution Calculator
C1V1 = C2V2 with the off-by-one made explicit — a 1:10 dilution takes nine parts of diluent, not ten, and the error is worst at small factors.
Both concentrations just need to share a unit — molar, percent, milligrams per millilitre. This also assumes volumes add, which is close enough for aqueous work and not true for everything: mixing ethanol and water gives less than the sum of the parts. Nothing is uploaded.
A 1:10 dilution takes nine parts of diluent, not ten
"1:10" names one part stock in a total of ten — so nine parts diluent, not ten. Adding ten to one gives 1:11, which is 10% weaker than intended and never announces itself. The rule is simply: parts of diluent equals the factor minus one.
| Dilution | Parts diluent | Adding the whole factor gives | Error |
|---|---|---|---|
| 1:2 | 1 | 1:3 | 50.00% |
| 1:5 | 4 | 1:6 | 20.00% |
| 1:10 | 9 | 1:11 | 10.00% |
| 1:20 | 19 | 1:21 | 5.00% |
| 1:100 | 99 | 1:101 | 1.00% |
| 1:1000 | 999 | 1:1001 | 0.10% |
And notice which way the error runs. It is worst at the small dilutions — half wrong at 1:2, a tenth at 1:10, a rounding error by 1:1000 — which is the opposite of where the worry usually goes. The mistake that matters is the two-fold one nobody checks, not the thousand-fold one everybody does.
And C1V1 = C2V2 reads four ways at once
To make 500 mL of 0.1 from 2, take 25 mL of stock and 475 mL of diluent. The dilution factor 20 is both the concentration ratio and the volume ratio, which is the whole of why the relation works.
| Target | Stock needed | Diluent | Factor |
|---|---|---|---|
| 1 | 250.00 mL | 250.00 mL | 2× |
| 0.5 | 125.00 mL | 375.00 mL | 4× |
| 0.2 | 50.00 mL | 450.00 mL | 10× |
| 0.1 | 25.00 mL | 475.00 mL | 20× |
| 0.05 | 12.50 mL | 487.50 mL | 40× |
| 0.01 | 2.50 mL | 497.50 mL | 200× |
Stock and diluent always sum to the final volume, which is the check worth doing in your head before you pipette anything. A target at the stock strength uses the whole volume and no diluent at all; a target above it is not a dilution, and the tool says so rather than returning a number that looks usable.
How to use
- Enter the stock concentration.
- Enter the target concentration in the same unit.
- Enter the final volume you want.
- Read the stock and diluent volumes, and the parts ratio.
Frequently asked questions
How do I dilute a stock solution?
C1V1 = C2V2. To make 500 mL of 0.1 M from a 2 M stock, take 25 mL of stock and 475 mL of diluent — the two always sum to the final volume, which is the check worth doing before pipetting.
Does a 1:10 dilution mean adding ten parts?
No — nine. "1:10" means one part stock in a total of ten, so the diluent is the factor minus one. Adding ten parts to one gives 1:11, which is 10% weaker than intended and never announces itself.
How bad is that off-by-one?
It depends on the factor, and not the way people expect. At 1:2 it is 50% wrong, at 1:10 it is 10%, and by 1:1000 it is a tenth of a percent. The trap is in the SMALL dilutions, not the big ones.
What exactly is the dilution factor?
The ratio of concentrations, and also the ratio of volumes — those being equal is the whole reason C1V1 = C2V2 works. A twentyfold dilution is a twentieth of the concentration and a twentieth of the volume as stock.
What if my target is stronger than my stock?
Then it is not a dilution and no amount of diluent will get there. The tool says so rather than returning a number that looks usable, because a silently wrong volume is worse than an error message.
Do the volumes really just add?
Close enough for aqueous work, and not universally true. Mixing ethanol and water gives less than the sum of the parts, so for non-aqueous or highly concentrated solutions you should make up to volume rather than adding a calculated diluent.
What units should I use?
Any, as long as both concentrations share one — molar, percent, milligrams per millilitre. The arithmetic is a ratio, so the units cancel and only the final volume carries a unit of its own.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.