About
C1V1 = C2V2 is the universal dilution equation. Used in chemistry, biology, pharmacy. Stock × stock_volume = final × final_volume. Most common: solve for V1 (volume of stock to take). Add solvent to V1 to reach V2.
What is Dilution Calculator?
A Dilution Calculator computes dilution from the inputs you provide. It applies the standard formula to the values you enter and returns the result instantly, without sending any data to a server. Free Dilution Calculator. The tool runs entirely in.
Dilution Calculator
C1V1 = C2V2. Solve for any variable.
Inputs
M
mL
M
mL
Result
-
Breakdown
Solvent to add
-
Dilution factor
-
Times diluted
-
Note
-
About the dilution equation
Diluting a solution means lowering its concentration by adding more solvent (usually water or buffer) without adding any more solute. The dilution equation C1V1 = C2V2 is the single most-used relationship in a wet lab, taught in every introductory chemistry and biology course and relied on daily by analytical chemists, microbiologists, molecular biologists, and pharmacists.
The four symbols are the concentration and volume on each side of the dilution. C1 and V1 describe the concentrated stock you start with; C2 and V2 describe the diluted working solution you want to end with. Because the equation has four variables and one constraint, fixing any three lets you solve for the fourth. In practice you almost always know C1 (printed on the bottle), C2 (what your protocol calls for), and V2 (how much working solution you need), and you solve for V1, the volume of stock to measure out.
This calculator solves for whichever variable you choose, then reports the dilution factor and the volume of solvent you must add to reach the final volume. It works for any concentration unit (molar, mg/mL, percent, X-fold buffer) as long as C1 and C2 share that unit.
How the formula works
The equation is a direct consequence of conservation of mass. Adding pure solvent changes the volume but not the number of moles (or grams) of solute, so the amount of solute before and after must be equal:
C1 x V1 = C2 x V2 (moles before = moles after) Solve for stock volume: V1 = (C2 x V2) / C1 Solve for final volume: V2 = (C1 x V1) / C2 Solvent to add: V_solvent = V2 - V1 Dilution factor: DF = C1 / C2 = V2 / V1
- C1 = stock concentration (the concentrated source). Higher C1 means you need less of it.
- V1 = volume of stock to take, the answer most protocols need.
- C2 = target working concentration. Must use the same unit as C1.
- V2 = final total volume after dilution, not the volume of solvent added.
- Dilution factor = how many times more dilute the result is. A factor of 10 is written 1:10.
Worked example
You have a 10 M stock of NaOH and need 50 mL of a 1 M working solution. Solve for V1, the volume of stock to pipette.
- Identify the knowns: C1 = 10 M, C2 = 1 M, V2 = 50 mL.
- Apply the formula: V1 = (C2 x V2) / C1 = (1 x 50) / 10.
- Compute: V1 = 50 / 10 = 5 mL of stock.
- Solvent to add: V2 - V1 = 50 - 5 = 45 mL of water.
- Dilution factor: C1 / C2 = 10 / 1 = 10, i.e. a 1:10 dilution.
Result: Measure 5 mL of the 10 M stock into a container, then add 45 mL of water to reach 50 mL total. The working solution is now 1 M, ten times more dilute than the stock.
Reference: common dilution factors
| Written as | Dilution factor | Stock per 100 mL final | Solvent per 100 mL final |
|---|---|---|---|
| 1:2 | 2x | 50 mL | 50 mL |
| 1:5 | 5x | 20 mL | 80 mL |
| 1:10 | 10x | 10 mL | 90 mL |
| 1:100 | 100x | 1 mL | 99 mL |
| 1:1000 | 1000x | 0.1 mL (use serial) | 99.9 mL |
Below roughly 1 to 2 mL of stock, switch to a serial dilution so each pipetted volume stays in the accurate range of your pipette.
Common pitfalls
- Confusing V2 with solvent volume. V2 is the total final volume. The solvent you add is V2 minus V1, not V2 itself. Bringing 5 mL of stock up to 50 mL means adding 45 mL, not 50 mL.
- Mismatched units. C1 and C2 must share a unit (both molar, or both mg/mL). Mixing molar with percent gives a meaningless answer.
- Pipetting impractically small volumes. A single-step 1:1000 dilution needs 0.1 mL per 100 mL, below most pipettes' accurate range. Use a two-step serial dilution (1:10 then 1:100) instead.
- Adding water to concentrated acid. Always add acid to water, never the reverse. The heat of dilution can boil and spatter. This is the one case where order is a safety matter, not just convention.
- Forgetting volume contraction. For highly concentrated mixtures (e.g. ethanol and water), final volume can be slightly less than the sum of parts. For typical aqueous lab dilutions the effect is negligible, but bring to volume in a volumetric flask when precision matters.
Related calculators
Frequently asked questions
What does C1V1 = C2V2 actually mean?
It is a conservation-of-moles statement. C1 is the concentration of your stock, V1 is the volume of stock you take, C2 is the concentration you want, and V2 is the final volume after adding solvent. Because the number of moles of solute does not change when you add only solvent, concentration times volume on the stock side must equal concentration times volume on the diluted side. Solving for V1 = (C2 x V2) / C1 tells you exactly how much stock to pipette.
How do I make a 1:10 dilution?
A 1:10 (one in ten) dilution means one part stock plus nine parts solvent for a total of ten parts. For 10 mL final volume, take 1 mL of stock and add 9 mL of solvent. The dilution factor is 10, so the final concentration is one tenth of the stock. Note the difference between 1:10 (one part in ten total) and 1+10 (one part stock to ten parts solvent, giving eleven parts total); laboratories use the in-total convention.
Do the units of C and V matter?
The two concentration units must match each other and the two volume units must match each other, but the system is unit-agnostic beyond that. You can use molar, millimolar, mg/mL, percent, or X-fold buffer for concentration as long as C1 and C2 use the same unit. Likewise mL and mL, or uL and uL, for volume. The ratios cancel, so the formula works for any consistent pair.
What is a serial dilution and when do I use one?
A serial dilution is a stepwise chain where the output of one dilution becomes the stock for the next, for example diluting 10-fold five times to reach a 100,000-fold total. You use it when a single-step dilution would require pipetting an impractically tiny volume (below about 1 to 2 uL), which pipettes cannot deliver accurately. Each step keeps volumes in a measurable range while the factors multiply.
Why add stock to solvent and not the other way around?
For most aqueous dilutions the order does not change the chemistry, but for concentrated acids the rule is to add acid to water, never water to acid. Diluting acid releases heat, and adding water to concentrated acid can boil and spatter. Adding acid slowly to a larger volume of water dissipates the heat safely. For non-hazardous solutions, add the calculated stock first, then bring to the final volume with solvent.