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What does this calculator estimate?
A dilution calculator solves the C1V1 = C2V2 equation for whichever value is missing. Leave one of the four fields blank — stock concentration, stock volume, final concentration, or final volume — and the tool computes it.
- C1V1 = C2V2
- Moles of solute stay constant during dilution
- Leave exactly one field blank
How dilution works
Dilution adds solvent without changing the amount of solute. Because moles are conserved, the product of concentration and volume is constant: C1V1 = C2V2. This is the standard equation for preparing working solutions from stock.
Limitations to watch for
The equation assumes volumes are additive and the solute behaves ideally — real solutions can contract or expand slightly on mixing. The tool requires exactly one unknown; if two fields are blank it can't solve. Units must be consistent on each side.
How to use it in practice
Decide the final volume and concentration you need, then compute the stock volume to pipette. Add stock first, then solvent up to the final volume. Always mix thoroughly after diluting.
['Fill in three of the four values (C1, V1, C2, V2).', 'Leave the one you want to find blank.', 'The tool solves C1V1 = C2V2 for the missing value.']
What dilution measures
Dilution is the reduction in concentration when a solvent is added to a solution: C1V1 = C2V2. A 5 mL stock at 10 mg/mL diluted to 50 mL total becomes 1 mg/mL. The calculator solves for any of the four variables.
The C1V1 = C2V2 equation
C1V1 = C2V2 states that the amount of solute is conserved: concentration times volume before equals concentration times volume after. Solving for the final concentration divides the initial solute amount by the final volume. It is the workhorse of lab math, used in nearly every preparation protocol.
Serial dilutions multiply
Each step of a serial dilution multiplies the previous concentration by the dilution factor: ten-fold three times is a 1,000-fold total reduction. The calculator handles single steps; the pattern is the multiplication of the factors.
Units must match
The equation works only when units are consistent: mixing mL with L or mg/mL with µg/mL produces wrong answers by orders of magnitude. Convert units first, then apply the equation — the calculator's unit handling prevents the most common lab error.
A worked example
To make 100 mL of 2 mM from a 20 mM stock: V1 = C2V2 ÷ C1 = (2 × 100) ÷ 20 = 10 mL of stock, plus 90 mL of solvent. The calculator returns the stock volume and the solvent volume so the protocol is complete.
How this calculator works
Formula
C1 × V1 = C2 × V2 (conservation of solute): concentration × volume before equals concentration × volume after. Given any three of C1, V1, C2, V2, the fourth is solved directly.
Worked example
Diluting a 5 M stock to make 500 mL of 1 M solution: V1 = (1 M × 0.5 L) ÷ 5 M = 0.10 L = 100 mL of stock, then add solvent to 500 mL.
Assumptions to verify
- Moles of solute are conserved (no reaction, no evaporation).
- Volumes are additive.
- Units are consistent across the equation.
Frequently asked questions
What is the dilution equation?
C1V1 = C2V2 — the concentration × volume before dilution equals concentration × volume after, because the amount of solute doesn't change.
How much stock do I need?
Solve V1 = (C2 × V2) ÷ C1. For 500 mL of 1 M from 5 M stock: V1 = 0.5 ÷ 5 = 0.1 L = 100 mL.
Why does the solute amount stay constant?
Dilution only adds solvent — it doesn't add or remove solute. So moles before = moles after.
What units should I use?
Any consistent units on both sides: liters with molarity, or mL with any concentration unit. Mixing liters and mL without conversion breaks the equation.
Do I add water to stock or stock to water?
For acids, add acid to water (not water to acid) to dissipate heat safely. For general dilutions, adding stock then solvent to the final mark is standard.
What if I leave two fields blank?
The equation has one degree of freedom — with two unknowns it's underdetermined. Fill three fields to solve the fourth.
Is dilution exact?
It's exact if volumes are measured accurately and are additive. Slight volume changes on mixing introduce small errors in precise work.
What is the dilution formula?
C1V1 = C2V2 — concentration times volume is conserved across the dilution.
How do I calculate final concentration?
C2 = C1V1 ÷ V2: 10 mg/mL × 5 mL ÷ 50 mL = 1 mg/mL.
What is a serial dilution?
Repeated dilutions that multiply the reduction factor each step.
Why do units matter?
Mixing unit systems changes the answer by orders of magnitude.
Cite this tool
BoringToolsKit. “Dilution Calculator (C1V1=C2V2).” boringtoolskit.com/dilution-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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