Dilution Calculator for C1V1 = C2V2
Solve a single volumetric or gravimetric dilution, calculate the dilution factor, or plan repeated serial dilution steps. Compatible units convert automatically, while exact decimal arithmetic preserves small differences and large dilution factors.
- Four-variable dilution solver
- Volumetric and gravimetric modes
- Serial dilution table
- Exact unit-aware arithmetic
Online Dilution and Stock Solution Calculator
Choose one method, select the unknown quantity and enter the known values. The calculator keeps concentration families separate and checks whether the result represents a real dilution rather than concentration by solvent removal.
The answer, dilution factor, normalized quantities and calculation steps will appear here.
Calculation Details
| Quantity | Selected value | Base value | Meaning |
|---|---|---|---|
| Dilution values | — | — | Enter values to begin. |
Calculation Steps
- Select a dilution method and enter the active known values.
- The calculator will normalize compatible units and apply the selected conservation equation.
How to Use This Dilution Calculator
- Choose the dilution method. Use volumetric mode for concentration per solution volume, gravimetric mode for mass fraction, or serial mode for repeated equal-factor steps.
- Select the unknown quantity. In a single dilution, choose C1, V1, C2 or V2, or the matching mass-based quantity.
- Choose one compatible concentration basis. Do not mix mol/L with g/L, mass fraction with volume, or different chemical entities.
- Enter each known value and unit. Use complete decimals or scientific notation without commas, formulas or unit symbols.
- Treat final volume as the complete solution volume. Transfer the calculated stock aliquot and make the solution up to the final mark.
- Calculate and review the checks. Confirm the dilution factor, unit conversions, nominal diluent difference and conservation equation.
- Verify the real procedure. Check solution compatibility, temperature, density assumptions, equipment limits, safety data and required laboratory controls.
The Dilution Formula
A simple dilution keeps the amount of the selected solute constant while increasing the total solution amount with a solute-free diluent. For a volume-based concentration, the conserved quantity is concentration multiplied by solution volume.
C1 is the initial stock concentration, V1 is the stock aliquot volume, C2 is the final concentration, and V2 is the final total solution volume. The equation works when both concentrations describe the same solute on the same compatible basis.
| Unknown | Rearranged formula | Typical question |
|---|---|---|
| Initial concentration, C1 | C1 = C2V2 / V1 | How strong was the stock? |
| Stock aliquot, V1 | V1 = C2V2 / C1 | How much stock should be transferred? |
| Final concentration, C2 | C2 = C1V1 / V2 | What concentration results after dilution? |
| Final volume, V2 | V2 = C1V1 / C2 | To what total volume should the solution be made up? |
The gravimetric mode uses the parallel relationship w1m1 = w2m2. Here w is solute mass fraction and m is total solution mass. Keeping it separate prevents the common error of multiplying a mass fraction by solution volume without density information.
Worked Dilution Example
Suppose you need 20 mL of a 50 µM solution from a 10 mM stock. Convert the concentrations to one unit first. A 10 mM stock equals 10,000 µM.
Transfer 100 µL of stock and make the complete solution up to 20 mL. The nominal volume difference is 19.9 mL. In accurate volumetric preparation, this difference is guidance rather than an instruction to assume that all liquid volumes add perfectly.
The dilution factor is 10,000 / 50 = 200. The final solution contains one two-hundredth of the initial concentration, and the stock aliquot represents 0.5% of the final nominal volume.
Dilution Factor, Fraction and Ratio
This page defines the dilution factor as the initial concentration divided by the final concentration. It is also final total volume divided by stock aliquot volume.
A factor of 10 means the final concentration is one tenth of the stock concentration. The dilution fraction is 1/10. On this page, a “1:10 dilution” means one part sample brought to ten total parts, which corresponds to nine nominal parts diluent. Some fields use ratio language differently, so record the definition with the result.
How Serial Dilution Works
A serial dilution repeats a step using material from the previous dilution. Equal step factors multiply. They do not add. If every step has factor d and the series contains n dilution steps, the cumulative factor is dn.
For four 1:10 steps, the cumulative factor is 10,000. A 1 M starting solution therefore reaches 0.0001 M, or 100 µM. If each receiving tube has a nominal final mixture volume of 1,000 µL, a 1:10 step transfers 100 µL and uses 900 µL diluent.
The table reports the concentration at every step from the original unrounded value. It also shows the transfer and nominal diluent volumes. If material is transferred onward from a tube, the usable volume remaining in that tube is lower than the mixture volume shown. Real serial dilution accuracy also depends on pipette calibration, mixing, wetting, carryover and the practical size of each transfer.
Compatible Concentration Units
The numerical equation is reliable only when the two concentration values describe the same quantity. The calculator converts within one selected family and blocks silent cross-family assumptions.
| Family | Examples | Important limit |
|---|---|---|
| Amount concentration | mol/L, mM, µM, nM, pmol/L | Needs molar mass to convert to mass concentration. |
| Mass concentration | g/L, mg/mL, mg/L, µg/mL, % w/v | Uses final solution volume, not solvent mass. |
| Number concentration | entities/L, entities/mL, entities/µL | The counted entity must stay the same. |
| Volume concentration | V component/V final solution, nominal % v/v, mL/L, µL/L | Uses component volume divided by final solution volume. This is not strict IUPAC volume fraction unless component volumes are additive. |
| Mass fraction | % w/w, g/kg, mg/kg, µg/kg | Use gravimetric mode with total solution mass. |
Do not treat molality as molarity. Molality uses amount of solute per mass of solvent, while molarity uses amount per final solution volume. Do not assume that 1 ppm always equals 1 mg/L. That shortcut needs a stated basis and density conditions.
Assumptions, Limits and Common Mistakes
- The same conserved solute must be present before and after dilution.
- No reaction, precipitation, adsorption, volatilization or solute loss is included.
- A pure dilution requires C2 not to exceed C1 and the final amount not to be below the initial amount.
- Equal initial and final values are valid, but they represent no dilution and a factor of 1.
- A nonzero stock cannot reach exactly zero concentration at a finite positive final volume.
- Final volume means the total prepared solution. It is not the volume of diluent alone.
- Mass fraction belongs with solution mass. Converting mass fraction to mass concentration requires density.
- pH, activity, osmolarity, normality and reactive mixtures need separate chemistry models.
- Displayed significant digits do not improve the accuracy of measured inputs or laboratory equipment.
- For hazardous materials, follow the chemical safety data sheet and an approved preparation procedure.
Inputs accept positive whole numbers, decimals and scientific notation with an exponent from −400 to 400. Each value is limited to 80 significant digits and 128 characters. Serial steps are limited to 50, and the per-step factor must be greater than 1 and no more than 1012. Exact rational arithmetic prevents normal floating-point cancellation, overflow and underflow inside these documented limits.
Related Calculators
Continue with a focused calculator when your problem needs a different mathematical or measurement model.
Dilution Calculator FAQs
What is the basic dilution formula?
The basic volumetric formula is C1V1 = C2V2. It states that the concentration-volume product for the conserved solute is the same before and after adding solute-free diluent.
How do I calculate the stock volume needed?
Rearrange the equation to V1 = C2V2/C1. Use compatible concentration units, then transfer V1 of stock and bring the complete solution to final volume V2.
Is final volume the same as diluent volume?
No. Final volume is the total volume of the prepared solution. The calculator shows V2 minus V1 as a nominal difference, but accurate preparation normally brings the solution to a final mark.
What does a 1:10 dilution mean here?
On this page, 1:10 means one part sample in ten total parts, so the dilution factor is 10 and the nominal diluent share is nine parts. Always state the convention because ratio wording varies.
How is dilution factor calculated?
Dilution factor equals C1/C2 and V2/V1 for a valid single dilution. A factor of 200 means the final concentration is one two-hundredth of the stock concentration.
How do serial dilution factors combine?
They multiply. Four equal tenfold steps have a cumulative factor of 10 to the fourth power, or 10,000. The final concentration is the starting concentration divided by that cumulative factor.
Can I mix mol/L with mg/mL?
Not directly. Converting amount concentration to mass concentration requires the molar mass of the exact chemical entity. Choose one compatible concentration family for this dilution calculation.
Can I use percent weight by weight with volume?
Not without density information. Use gravimetric mode for mass fraction and total solution mass. Converting mass fraction to a volume-based concentration requires an appropriate solution density.
Why does the calculator reject a target stronger than the stock?
Adding solute-free diluent cannot increase concentration. A stronger target requires added solute, solvent removal or another concentration process, so it is outside a pure dilution model.
Should I use this result as a laboratory procedure?
No. Treat it as calculation support. Verify chemical identity, purity, compatibility, temperature, density, equipment limits, safety data and the approved procedure before preparing a real solution.
Method and Review Basis
The volumetric equation and final-volume meaning were checked against OpenStax Chemistry 2e and the FDA Elemental Analysis Manual dilution guidance. Unit symbols and litre relationships were checked against NIST volume guidance. Concentration terminology follows the IUPAC amount concentration definition, IUPAC mass concentration definition, IUPAC number concentration definition and IUPAC mass fraction definition. IUPAC defines volume fraction using the sum of component volumes before mixing, so the page labels V component divided by final solution volume as volume concentration instead.
Educational and laboratory-planning disclaimer: This calculator provides mathematical results from the values you enter. It is not a validated laboratory method, medical dosing instruction, safety procedure or substitute for qualified review. Confirm units, assumptions, measurement uncertainty and chemical safety before practical use.