Quick answer: This dilution calculator (C1V1 = C2V2) is built on the rule that diluting keeps the moles of solute fixed, so C1V1 = C2V2. Enter any three of the four values (initial/final concentration and volume) and the calculator solves for the fourth, plus the dilution factor and solvent to add.
Last reviewed: September 2026
Key facts
- C1V1 = C2V2 — dilution never changes the moles of solute, only the volume.
- Rearranged: V1 = C2V2 ÷ C1 is the most-used bench form (stock volume to pipette).
- Dilution factor = C1 ÷ C2 = V2 ÷ V1.
- Units must match on each side: both concentrations in one unit, both volumes in one unit.
Diluting a solution adds solvent without changing the amount of dissolved solute, so concentration times volume stays constant: C1V1 = C2V2. This free dilution calculator (C1V1) solves for any one of the four variables from the other three and reports the dilution factor and the solvent volume to add.
Pick the value to solve for, enter the three known values with matching units, and get the bench-ready answer. No sign-up, works on mobile and desktop.
How to use this dilution calculator (C1V1)
- Choose what to solve for — usually V1, the stock volume you need.
- Pick a concentration unit and a volume unit; both fields of each type must use the same unit.
- Enter the three known values; the unknown field is ignored.
- Read the answer plus the dilution factor and solvent to add.
Background: dilution in science
Dilution is one of the oldest quantitative operations in chemistry: a concentrated stock solution is turned into a working solution by adding solvent. Because the amount of solute does not change — only the volume it occupies — the product of concentration and volume is conserved, which is the physical insight behind C1V1 = C2V2.
The technique became indispensable as analytical chemistry matured in the 19th century, when reagents began to be supplied as concentrated stocks and diluted at the bench. It remains central in several fields today: in pharmacy and medicine, concentrated drug solutions are diluted to safe, measurable doses before administration; in microbiology, serial dilution underpins colony counting and the determination of bacterial and viral titers; and in analytical chemistry, samples are routinely diluted to bring them into the working range of instruments such as spectrophotometers.
Single-step vs serial dilution
A dilution calculator c1v1 solver handles the arithmetic either way, but the bench strategy matters:
| Single-step dilution | Serial dilution | |
|---|---|---|
| What it is | One jump from stock to target (e.g. 10 M → 1 M) | A chain of equal dilutions (e.g. 10 M → 1 M → 0.1 M → 0.01 M) |
| Best for | Moderate factors (up to ~100×) | Very large factors (1,000× and beyond) |
| Pipetting | May require awkward tiny volumes | Each step uses comfortable, measurable volumes |
| Accuracy | One measurement step | Errors can compound across steps; mix well and use calibrated pipettes |
When a single step would need 0.1 mL of stock for 100 mL final, two 10× serial steps (10 mL → 100 mL, then 10 mL of that → 100 mL) are usually more accurate in practice.
The dilution equation
| Term | Meaning |
|---|---|
| C1 | Initial (stock) concentration. |
| V1 | Initial volume — the stock volume to use. |
| C2 | Final (target) concentration. |
| V2 | Final volume — the total after dilution. |
| DF | Dilution factor = C1 ÷ C2 = V2 ÷ V1. |
| Vsolvent | Solvent to add = V2 − V1. |
Because the ratio is what matters, the equation works in any consistent units: M with L, mg/mL with mL, % with µL.
Dilution notation: 1:10 vs 10×
| Notation | Meaning | Example |
|---|---|---|
| 10× (ten-fold) | Dilution factor 10: final is one-tenth as concentrated | 10 M → 1 M |
| 1:10 | Ambiguous; the common lab reading is "1 part in 10 total" | 1 mL stock + 9 mL solvent = 10 mL total |
| 1/10 | One-tenth the original concentration | Same as 10× |
This calculator reports the dilution factor as DF = C1 ÷ C2, avoiding the "1:10" ambiguity — always check whether a protocol means 1 part stock in 10 total, or 1 part stock plus 10 parts solvent.
Worked examples
Make 100 mL of 1 M from 10 M stock
V1 = C2 × V2 ÷ C1 = 1 × 100 ÷ 10.
V1 = 10 mL of stock, add 90 mL of solvent. Dilution factor 10×.
Dilute 25 mL of 0.5 M to 250 mL
C2 = C1 × V1 ÷ V2 = 0.5 × 25 ÷ 250.
C2 = 0.05 M (50 mM), a 10× dilution.
Prepare 100 mL of 5 mg/mL from 20 mg/mL stock
The dilution calculator c1v1 result: V1 = C2 × V2 ÷ C1 = 5 × 100 ÷ 20.
V1 = 25 mL of stock, then add solvent to a total of 100 mL. Dilution factor 4×.
Dilution factor quick table
| Stock | Target | Factor | For 100 mL final |
|---|---|---|---|
| 10 M | 1 M | 10× | 10 mL stock + 90 mL solvent |
| 1 M | 0.1 M | 10× | 10 mL stock + 90 mL solvent |
| 100 mg/mL | 10 mg/mL | 10× | 10 mL stock + 90 mL solvent |
| 1 M | 1 mM | 1000× | 0.1 mL stock + 99.9 mL solvent |
Limitations and assumptions
- Volumes are treated as additive. In reality, mixing can contract slightly (notably ethanol–water mixtures), so high-precision work should verify the final concentration after dilution.
- Mixing is assumed complete. Always mix thoroughly before using the diluted solution; an unmixed gradient gives a wrong concentration at the top and bottom.
- Concentration basis must match. The tool works with any consistent pair of units, but it cannot convert between mass and molar concentration — that needs the molar mass.
- Very large factors are better done serially. A single 1,000× step magnifies one pipetting error; serial 10× steps distribute the error.
Frequently asked questions
What is the C1V1 = C2V2 formula?
It is the dilution equation: initial concentration times initial volume equals final concentration times final volume. Adding solvent changes the volume but not the moles of solute, so the product C × V is conserved.
How much stock solution do I need?
Use V1 = C2 × V2 ÷ C1. Example: to make 100 mL of 1 M from 10 M stock, V1 = 1 × 100 ÷ 10 = 10 mL of stock, then add 90 mL of solvent.
What is the dilution factor?
The dilution factor is C1 ÷ C2, which also equals V2 ÷ V1. A 10× dilution means the final solution is one-tenth as concentrated (a 1:10 dilution).
Do the units have to match?
Yes — both concentrations must share one unit and both volumes must share one (possibly different) unit. Because the equation is a ratio, the actual unit cancels, so M, mM, mg/mL or % all work as long as they match on both sides.
Why is my diluted solution's concentration slightly off?
Common causes: measuring stock by volume imprecisely, not mixing after adding solvent, or using V as the solvent volume instead of the total final volume. For critical work, verify by spectrophotometry or titration.
Sources
- LibreTexts: Solution Dilution — the dilution equation C1V1 = C2V2 with worked examples
- OpenStax: Chemistry 2e — free college chemistry textbook covering solution concentration and dilution
Key takeaways
- C1V1 = C2V2 because dilution conserves moles of solute.
- V1 = C2V2 ÷ C1 gives the stock volume to pipette.
- Dilution factor = C1 ÷ C2; solvent to add = V2 − V1.
- Keep concentration units matched and volume units matched.
- For very large dilution factors, dilute in serial steps rather than one extreme jump.
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