Calculation details
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What does this calculator estimate?
A C1V1 = C2V2 calculator solves for the missing dilution value. Leave one of the four fields blank — initial concentration, initial volume, final concentration, or final volume — and the tool computes it.
- C1V1 = C2V2
- Moles of solute are conserved
- Leave exactly one field blank
How the dilution equation works
The product of concentration and volume equals the moles of solute. Dilution adds solvent but doesn't change moles, so C1V1 stays equal to C2V2 before and after. It's the standard equation for making working solutions.
Limitations to watch for
The equation assumes additive volumes and ideal behavior. Units must be consistent on each side — mix mL and L and the result is wrong. With two unknowns it can't solve; fill exactly three fields.
How to use it in practice
Decide the final volume and concentration, then compute the stock volume to pipette. Add stock first, then solvent up to the final mark. For acids, always add acid to water.
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The dilution equation
C1V1 = C2V2 states that the amount of solute is conserved: concentration × volume before equals concentration × volume after. Diluting 10 mL of 20 mM stock to a final 50 mL gives 4 mM. The calculator solves for any variable.
When to use it
The equation covers stock dilutions, serial dilutions, and solution preparation — the daily math of labs. It works for any concentration unit as long as both sides match: M, mM, mg/mL, percent, and others.
Units must be consistent
The most common error is mixing units: 20 mM stock diluted into mL final volume must use the same concentration unit throughout. Convert first, then solve. The calculator's explicit inputs prevent the classic 1,000× error.
A worked example
To make 100 mL of 2 mM from a 20 mM stock: V1 = C2V2 ÷ C1 = (2 × 100) ÷ 20 = 10 mL stock + 90 mL solvent. The calculator returns both volumes so the protocol is complete and correct.
Serial dilution patterns
Each step multiplies the dilution factor: ten-fold twice is 100-fold total. The equation applies at each step; the calculator handles single steps and the pattern is simple multiplication.
How this calculator works
Formula
C1 × V1 = C2 × V2 (conservation of moles). Given any three of the initial concentration, initial volume, final concentration, and final volume, the fourth is solved.
Worked example
Diluting a 6 M stock to make 500 mL of 0.5 M: V1 = (0.5 × 0.5) ÷ 6 = 0.0417 L = 41.7 mL of stock, then add solvent to 500 mL.
Assumptions to verify
- Moles of solute are conserved.
- Volumes are additive.
- Units are consistent across the equation.
Frequently asked questions
What is C1V1 = C2V2?
The conservation equation for dilutions: initial concentration × volume equals final concentration × volume, because solute moles don't change.
How do I find the stock volume?
V1 = (C2 × V2) ÷ C1. For 500 mL of 0.5 M from 6 M stock: V1 = 0.25 ÷ 6 = 0.0417 L = 41.7 mL.
What units should I use?
Consistent units on both sides — mL with any concentration, or L with molarity. Mixing units breaks the equation.
Why is solute conserved?
Dilution only adds solvent; it neither creates nor destroys solute. So moles before = moles after.
How is this different from the dilution calculator?
It's the same equation — this tool is the standalone version with the same four-field solver.
What if I leave two fields blank?
The system is underdetermined — fill three values to solve the fourth.
Does this apply to serial dilutions?
Each single step follows C1V1 = C2V2; the serial dilution calculator chains multiple steps automatically.
What is the C1V1 = C2V2 formula?
Concentration × volume before equals concentration × volume after — solute is conserved.
Do units have to match?
Yes — inconsistent units change the answer by orders of magnitude.
Does it work for serial dilutions?
Yes, step by step — each step multiplies the previous dilution factor.
Cite this tool
BoringToolsKit. “C1V1 = C2V2 Calculator.” boringtoolskit.com/c1v1-c2v2-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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