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C1V1 Calculator

C1V1 = C2V2 is the dilution equation: the amount of solute you take from the stock equals the amount in the final solution. Enter any three of the four values and this calculator solves the fourth — most often the stock volume V1 you need to pipette — and also reports how much diluent to add. Concentrations can be entered in M, mM, µM, nM or pM and volumes in L, mL, µL or nL, mixed freely, because everything is normalised to mol/L and litres internally.

If you only learn one equation for the bench, make it C1V1 = C2V2. It answers the question you actually ask before a pipette ever leaves the rack: "I have a 100 mM stock and I need 50 mL of 10 mM — how much stock do I take?" It lives in our laboratory calculator set and is the precise, four-variable counterpart to the factor-based dilution calculator. Where that tool thinks in "1:X" ratios, this one thinks in concrete concentrations and volumes.

The reason the equation works is conservation: diluting adds solvent, not solute, so C1 × V1 (moles taken from the stock) must equal C2 × V2 (moles in the finished solution). Everything else is rearranging. If you want to see how the same idea underpins concentration itself, what is molarity walks through moles per litre, and the molarity calculator handles making the stock in the first place.

Stock volume V15 µL
C1 (stock)100 mM
C2 (final)10 µM
V1 (stock)5 µL
V2 (final)50 mL
Diluent to add49.995 mL

How to use the c1v1 calculator

Pick the unknown in the **Solve for** dropdown. The default solves for V1, the volume of stock to transfer — by far the most common case. The other modes solve for the final concentration C2, the required stock strength C1, or the final volume V2.

Enter the three values you know, each with its own unit. You can mix them: a stock in mM, a target in µM and a final volume in mL all solve correctly, because the engine converts every concentration to mol/L and every volume to litres before doing the arithmetic.

Leave the field you are solving for blank or ignored — it is hidden once you choose the mode. The calculator validates that the target concentration is not higher than the stock and that the stock volume does not exceed the final volume, catching the two most common setup slips.

Press **Calculate**. The primary card gives the unknown; the secondary cards restate C1, V1, C2 and V2 in canonical units and add the diluent volume (V2 − V1), which is the number you actually pipette second.

C1V1 formula

C₁V₁ = C₂V₂
V₁ = C₂V₂ / C₁
C₂ = C₁V₁ / V₂
C₁ = C₂V₂ / V₁
V₂ = C₁V₁ / C₂
V_diluent = V₂ − V₁
C₁ = stock concentration · V₁ = stock volume transferred · C₂ = final concentration · V₂ = final total volume. Concentrations share a basis; volumes share a basis.

Variables and units

SymbolMeaningUnit
C₁Stock (initial) concentrationmol/L
V₁Volume of stock transferredL
C₂Final concentrationmol/L
V₂Final total volumeL
V_diluentDiluent added (V₂ − V₁)L

How c1v1 is calculated

  1. Convert each concentration to mol/L (1 mM = 0.001 M, 1 µM = 1×10⁻⁶ M) and each volume to litres.
  2. Identify the unknown and rearrange C₁V₁ = C₂V₂ to isolate it.
  3. Substitute the three known canonical values and compute the fourth.
  4. Convert the answer back to a convenient unit and subtract V₁ from V₂ to get the diluent volume to add.

Worked laboratory examples

Example 1 — Stock volume for 50 mL of 10 mM from a 100 mM stock

Given: C₁ = 100 mM · C₂ = 10 mM · V₂ = 50 mL

  1. V₁ = C₂V₂ / C₁
  2. V₁ = (10 × 50) / 100 = 5 mL
  3. V_diluent = 50 − 5 = 45 mL

Result: pipette 5 mL of stock and add 45 mL of diluent

Example 2 — Mixed units: µM target from an mM stock

Given: C₁ = 5 mM · C₂ = 250 µM = 0.25 mM · V₂ = 10 mL

  1. V₁ = (0.25 × 10) / 5 = 0.5 mL
  2. V₁ = 500 µL
  3. V_diluent = 10 − 0.5 = 9.5 mL

Result: 500 µL of 5 mM stock into 9.5 mL of diluent

Example 3 — Final concentration after diluting a stock

Given: C₁ = 2 M · V₁ = 25 mL · V₂ = 500 mL

  1. C₂ = C₁V₁ / V₂
  2. C₂ = (2 × 25) / 500 = 0.1 M
  3. 0.1 M = 100 mM

Result: the final solution is 0.1 M (100 mM)

How to interpret the result

The solved value is the missing piece of a conserved-solute balance. When you solve for V1, read it as "this much of your stock contains exactly the moles that will end up in the final volume." The diluent card turns that into the second pipetting step, so you leave the calculator with a complete instruction rather than a single number.

The validation guards are the quiet value here. If C2 comes out higher than C1 you have asked to dilute upward, which is impossible from that stock; if V1 exceeds V2 you have asked to fit more stock than the final volume. Both are caught before a result is shown, instead of returning a negative diluent volume that is easy to miss.

Assumptions

  • Solute is conserved — dilution adds solvent only, with no reaction, binding, adsorption or evaporation loss.
  • C1 and C2 are on the same concentration basis (both molar here) and V1 and V2 on the same volume basis.
  • Volumes are additive; the final volume equals stock plus diluent.

Limitations

  • Concentration is handled in molar units (M to pM). For % w/v, mg/mL or CFU/mL dilutions, the ratio-based dilution calculator is the right tool.
  • Non-additive volume effects in concentrated or viscous solutions are not modelled; make up to a volumetric mark for analytical accuracy.
  • Results are estimates — your protocol, reagent purity and manufacturer guidance take precedence.

Common mistakes

  • Forgetting to convert units before substituting — entering C₁ in M and C₂ in mM as raw numbers throws the answer off by 1000×. This calculator converts for you, but the habit matters when you do it by hand.
  • Solving for V₁ but then adding it to V₂ of diluent instead of making the total up to V₂. V₁ + diluent must equal V₂.
  • Using the final volume as V₁ when you meant the stock volume. Keep the subscripts straight: 1 is stock, 2 is final.
  • Asking for a final concentration above the stock strength and wondering why the volume is negative — you cannot dilute to something stronger.

FAQ

What is the C1V1 = C2V2 equation?

It is the dilution equation. C1 and V1 are the concentration and volume of the stock you take; C2 and V2 are the concentration and volume of the final diluted solution. Because dilution conserves solute, C1V1 equals C2V2, and you can rearrange it to solve for whichever of the four is unknown.

How do I calculate how much stock to add?

Solve for V1: V1 = C2V2 / C1. For 50 mL of 10 mM from a 100 mM stock, V1 = (10 × 50) / 100 = 5 mL. Add diluent to reach the full 50 mL, which means 45 mL of diluent.

Can I mix mM and µM, or mL and µL?

Yes. Enter each value in its natural unit and the calculator normalises every concentration to mol/L and every volume to litres before solving, then converts the answer back. A 5 mM stock and a 250 µM target solve correctly without you converting first.

What is the difference between C1V1 and a dilution factor?

The dilution factor is the single ratio C1/C2 (or V2/V1), while C1V1 = C2V2 keeps all four quantities explicit. A factor of 10 and "100 mM to 10 mM" are the same dilution; use the factor form for 1:X thinking and this equation when you need specific volumes.

Why does the calculator reject C2 greater than C1?

Because you cannot make a solution more concentrated by diluting it. If the target exceeds the stock, either you are concentrating rather than diluting, or the two concentrations were entered the wrong way round.

Do I add V1 to V2 of diluent?

No. V2 is the final total volume. You transfer V1 of stock and then add diluent until the total reaches V2, so the diluent volume is V2 − V1. Adding V1 to V2 of diluent would overshoot the target concentration.

Scientific Sources

External links open in a new tab and carry rel="nofollow". We cite primary references (NIST, NIH/NCBI, peer-reviewed papers) and established manufacturer technical documentation (NEB, Thermo Fisher, Promega, IDT). Calculated results are estimates; your protocol and manufacturer guidance take precedence.

Last reviewed: 2026-09 · Method version: 1.0