Dilution Calculator
Solve for any unknown in C1V1 = C2V2: stock volume, final volume, stock concentration, or target concentration. Choose your concentration units (nM to M, mg/mL, or %) and volume units (nL to L). Enable serial dilution mode to see the concentration at every step in a scrollable table.
Formula
Worked example
To make 100 mL of 1 M NaCl from a 10 M stock: V1 = (1 M x 100 mL) / 10 M = 10 mL stock, plus 90 mL water (dilution factor 10x). To find what final volume 5 mL of a 100 mM stock gives at 10 mM: V2 = (100 mM x 5 mL) / 10 mM = 50 mL.
The dilution equation and why it always works
Every dilution calculation rests on one principle: the number of moles of solute does not change when you add solvent. Moles equals concentration times volume, so C1 times V1 (moles in the stock) must equal C2 times V2 (moles in the diluted solution). This gives C1V1 = C2V2, which rearranges to solve for any one of the four variables given the other three. The calculator does this algebra for you in all four directions: find the stock volume to pipette (V1), find the final volume you can make (V2), back-calculate the stock concentration needed (C1), or find what concentration a given mix produces (C2).
Concentration units and volume units
The equation is unit-agnostic, both C1 and C2 must simply be in the same unit. This calculator supports molar units from nM (nanomolar, 10^-9 M) through uM, mM, and M, as well as mg/mL and percent (w/v or v/v). Volume units range from nL to L. Because C1V1 = C2V2 is a ratio, a 10 M stock diluted to 1 M in molarity is identical algebra to a 10% stock diluted to 1% in percent, or a 10 mg/mL stock diluted to 1 mg/mL. Just keep the units consistent. For molar solutions the dilution factor (C1/C2) tells you the fold-dilution: a dilution factor of 10 means the final solution is ten times less concentrated than the stock.
Serial dilutions for large dilution factors
When the dilution factor exceeds roughly 100-fold, a single pipetting step becomes impractical because you are measuring a very small volume of stock relative to the total. Serial dilution splits the overall dilution into equal successive steps. For example, a 1,000,000-fold total dilution can be achieved by six sequential 10-fold dilutions (10^6). At each step you transfer a fixed volume from the previous tube into fresh solvent. Enable the serial dilution table to see the concentration at each step for the dilution factor implied by your C1 and C2 inputs. The cumulative dilution factor column shows how far from the original stock you are at each stage.
Practical laboratory tips
Always add the solute or stock to the solvent, never the reverse, especially for concentrated acids and bases where the heat of mixing is significant. Use a calibrated volumetric flask and bring the solution to the final volume mark rather than simply adding the calculated solvent volume: this corrects for the small volume change that occurs on mixing. For hygroscopic or volatile solutes, weigh and dissolve quickly to avoid concentration errors from moisture absorption or evaporation. Verify the concentration of a freshly prepared stock by a second method (UV absorbance, titration, or a refractometer) whenever precision matters.
Limitations
C1V1 = C2V2 assumes that volumes are strictly additive, which is a good approximation for dilute aqueous solutions but can fail for concentrated alcohol, strong acid, or salt solutions where mixing causes a volume change. The equation cannot correct for degradation of the stock solution, temperature-dependent density changes in percent w/v solutions, or the volume of any added solid. C2 must always be less than or equal to C1: you cannot concentrate a solution by dilution alone. For serial dilutions, small pipetting errors multiply across steps, so use calibrated pipettes and pre-mix each dilution thoroughly before transferring to the next tube.
Common concentration units at a glance
| Unit | Definition | Typical use | Conversion to M |
|---|---|---|---|
| nM | nanomolar = 10^-9 mol/L | Hormones, nanobody binding assays | x 10^-9 |
| uM | micromolar = 10^-6 mol/L | Drug IC50, enzyme Km | x 10^-6 |
| mM | millimolar = 10^-3 mol/L | Buffer components, metabolites | x 10^-3 |
| M | molar = mol/L | Stock acids, saline | 1 |
| mg/mL | mass per volume | Protein, antibody stocks | divide by MW (g/mol) |
| % | g/100 mL (w/v) or mL/100 mL (v/v) | Gels, disinfectants, alcohol | x 10 / MW for w/v |
All values are for aqueous solutions at room temperature. "Base" is the unit the calculator converts through internally.
Frequently asked questions
What is the dilution equation C1V1 = C2V2?
C1V1 = C2V2 expresses conservation of moles: concentration times volume gives moles, and the moles of solute do not change when you add solvent. C1 is the stock concentration, V1 is the stock volume used, C2 is the final concentration, and V2 is the final volume. Rearranging gives a formula for whichever variable you need.
How do I solve for C1 or C2, not just V1?
Use the "Solve for" dropdown to pick any of the four variables. For C1, enter C2, V1, and V2 and the calculator rearranges to C1 = (C2 x V2) / V1. For C2, enter C1, V1, and V2 and the calculator solves C2 = (C1 x V1) / V2. This is useful when you know the volumes and one concentration and want to find the other.
What is the dilution factor?
The dilution factor is C1 divided by C2, the ratio of stock concentration to final concentration. A dilution factor of 10 means the final solution is 10 times more dilute than the stock. It equals V2 divided by V1 by the same equation. Dilution factors above 100 are typically handled as serial dilutions.
What is a serial dilution and when do I need one?
A serial dilution is a sequence of equal-step dilutions where each tube is made by transferring a fixed volume from the previous one into fresh solvent. It is used when the total dilution factor is too large to achieve accurately in a single step (typically above 1:100) because the stock volume becomes too small to pipette accurately. Enable serial dilution mode to see the concentration at each step for your dilution factor.
Can I use percent (%) or mg/mL instead of molarity?
Yes. Select the appropriate unit in the "Concentration unit" dropdown. C1 and C2 must be in the same unit, but C1V1 = C2V2 is entirely unit-agnostic for ratios. A 10% stock diluted to 1% has the same algebra as a 10 M stock diluted to 1 M.
How much water do I add to dilute a solution?
First calculate V1 (the stock volume) using V1 = (C2 x V2) / C1. The solvent to add is V2 minus V1. However, always make up to the final volume mark in a volumetric flask rather than simply pouring in the calculated solvent volume: volumes are not always perfectly additive, and using a mark ensures accuracy.