Dilution calculator

The dilution equation: C1V1 = C2V2

A dilution changes concentration by increasing the solution volume while keeping the amount of solute constant. Let C₁ be the stock concentration, V₁ the stock volume you take, C₂ the target concentration and V₂ the final solution volume. Rearranging C₁V₁ = C₂V₂ gives V₁ = C₂V₂ / C₁.

Enter the three known quantities above. The calculator converts compatible concentration and volume units, gives the stock volume, and displays the nominal difference between final and stock volumes. It also shows the dilution factor, defined here as stock concentration divided by target concentration. A 100-fold dilution has one part stock in 100 parts final solution.

Worked example: 10 mM stock to 100 µM

Suppose you need 1 mL of a 100 µM solution from a 10 mM stock. First express both concentrations in the same units: 10 mM is 10,000 µM. The dilution factor is 10,000 / 100 = 100. The required stock volume is therefore 1 mL / 100 = 10 µL.

Bring that stock aliquot to a final volume of 1 mL. If the volumes are additive, the nominal diluent volume is 990 µL. A preparation requiring accurate final volume should follow the appropriate volumetric method rather than assuming all liquid volumes add exactly.

Compatible units, without hidden conversions

M, mM, µM and nM describe molar concentration. The calculator also accepts mg/mL, µg/mL, ng/µL and % w/v as mass-per-volume units. For example, 1 ng/µL equals 1 µg/mL, and 1% w/v means 1 g per 100 mL, or 10 mg/mL. It also accepts % v/v for liquids diluted by volume, and X for concentrated buffers: a 10X stock diluted to 1X is a tenfold dilution. Stock and target must both belong to the same kind of unit.

Converting a mass concentration to molarity requires the solute's molar mass. This tool refuses to make that conversion implicitly; the molarity calculator converts µg/mL or mg/mL to molarity when you enter the molar mass. % v/v and % w/v are not interchangeable without a density, and activity and optical-density units are not included here.

Primer resuspension and working dilution

A dried oligo has an amount, not a stock concentration. Start with the delivered quantity on its specification sheet and use V = n / C. In common lab units, volume in µL = amount in nmol × 1,000 / concentration in µM. The example below follows IDT’s resuspension example: 20.3 nmol at 100 µM gives 203 µL.

For a working solution, add the target concentration and final volume. For example, 100 µL at 10 µM takes 10 µL of a 100 µM stock and a nominal 90 µL of diluent. The calculator also shows how much stock remains and rejects a plan requiring more than the resuspended amount. These are calculation examples, not recommended concentrations or a buffer protocol.

When a single dilution is not enough

The target cannot be more concentrated than the stock. Equal concentrations need no dilution. Very small calculated aliquots may be difficult to measure with your equipment; an intermediate stock can make the preparation more practical. For a repeated dilution series, use the serial dilution calculator. Its mixed-versus-retained-volume example explains why transferring solution onward leaves less in a tube without changing its concentration. This page calculates a single stock-to-target step; neither tool estimates a pipette's accuracy.

If each dilution needs a fixed amount for later measurements, plan from the volume you need left. The worksheet allows for onward transfers and shows any final-tube discard.

The underlying solute-conservation relation is covered in OpenStax Chemistry 2e. The equation assumes no solute loss or chemical reaction. Save calculation records the entered units and current result for your own notes.

For a cell suspension measured with a counting chamber, use the hemocytometer calculator. It converts individual square counts to cells per mL and keeps viable-cell dilution targets separate from total-cell targets. For a protein stock, measure its concentration first with the protein concentration calculator, which turns an A280 reading into mg/mL and µM.

If your unmodified oligo amount is given by mass, the oligo calculator converts it to moles using the sequence and explicit end assumptions. For modified oligos, use your supplier’s molecular weight.