Last updated: July 3, 2026
Solution Dilution Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The solution dilution calculator solves the equation C1V1 = C2V2 for one missing variable among stock concentration, stock volume, final concentration, and final volume. For preparing a diluted working solution, stock volume is V1 = (C2 × V2) / C1, and solvent to add is V2 − V1.
For solution dilution, use C one V one equals C two V two. To find stock volume, multiply the desired final concentration by the final volume and divide by the stock concentration. Then subtract the stock volume from the final volume to estimate solvent to add.
Key Takeaways
- Simple solution dilution follows C₁V₁ = C₂V₂.
- To find stock volume, use V₁ = (C₂ × V₂) / C₁.
- Solvent to add equals final volume minus stock volume when volumes are compatible.
- Use matching concentration units and matching volume units before calculating.
- C₂ greater than C₁ is not achievable by dilution with solvent alone.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
C1 × V1 = C2 × V2; V1 = (C2 × V2) / C1; solvent to add = V2 − V1
Where:
- C1=Stock concentration(any concentration unit)
- V1=Stock volume needed(mL or L)
- C2=Final concentration(same as C1)
- V2=Final solution volume(same as V1)
- Vsolvent=Volume of solvent to add(same as V1)
Worked Examples
Prepare 500 mL of 1 M solution from 10 M stock
Find the stock volume and solvent needed for a ten-fold concentration dilution.
- 1Use V1 = (C2 × V2) / C1.
- 2Substitute: V1 = (1 M × 500 mL) / 10 M = 50 mL.
- 3Solvent to add = V2 − V1 = 500 − 50 = 450 mL.
Find final concentration after dilution to 100 mL
Dilute 20 mL of a 5 M stock to a final volume of 100 mL.
- 1Use C2 = (C1 × V1) / V2.
- 2Substitute: C2 = (5 M × 20 mL) / 100 mL.
- 3The final concentration is 1 M.
Calculate stock volume for a 0.5 M working solution
Make 250 mL of 0.5 M solution from a 2 M stock.
- 1Use V1 = (C2 × V2) / C1.
- 2Substitute: V1 = (0.5 M × 250 mL) / 2 M.
- 3The stock volume needed is 62.5 mL.
Introduction
The solution dilution calculator uses the classic conservation relationship C₁V₁ = C₂V₂. It solves for any one missing variable among stock concentration, stock volume, final concentration, and final volume, then reports the solvent volume to add when V₁ and V₂ are known. Use it with the dilution factor calculator for fold dilutions and the molarity calculator when concentrations are in mol/L. The equation follows standard IUPAC amount concentration ideas and common solution-preparation practice described in LibreTexts solution chemistry.
What is solution dilution?
Solution dilution lowers a solute concentration by adding solvent while keeping the amount of solute transferred from the stock solution constant. Because the moles or mass of solute in the aliquot do not change during dilution, the product of concentration and volume before dilution equals the product after dilution.
C₁ is the stock concentration.
V₁ is the stock volume transferred.
C₂ is the desired or resulting final concentration.
V₂ is the final total solution volume, not just the solvent volume.
C1V1 equals C2V2 formula explained
The working equation is C₁V₁ = C₂V₂. To find stock volume, rearrange to V₁ = (C₂ × V₂) / C₁. To find final concentration, use C₂ = (C₁ × V₁) / V₂. The concentration units cancel as long as C₁ and C₂ use the same unit, and the volume units cancel as long as V₁ and V₂ use the same unit.
The calculator treats exactly one blank or non-positive variable as the unknown and solves it from the other three positive values.
How to calculate a solution dilution
Enter any three of C₁, V₁, C₂, and V₂. Leave the variable you want to solve blank. For the common preparation task, enter stock concentration, desired final concentration, and desired final volume; the calculator returns the volume of stock solution to pipette and the solvent volume to add.
Choose matching concentration units, such as M and M or mg/mL and mg/mL.
Choose matching volume units, such as mL and mL or L and L.
Calculate V₁ from (C₂ × V₂) / C₁.
Add solvent until the total solution reaches V₂, so solvent = V₂ − V₁.
Common solution dilution examples
The table shows typical direct dilutions prepared by transferring stock solution into a volumetric flask and filling to the final mark.
| Stock C1 | Target C2 | Final V2 | Stock V1 | Solvent to add |
|---|---|---|---|---|
| 10 M | 1 M | 500 mL | 50 mL | 450 mL |
| 2 M | 0.5 M | 250 mL | 62.5 mL | 187.5 mL |
| 100 mM | 10 mM | 10 mL | 1 mL | 9 mL |
| 5 mg/mL | 1 mg/mL | 100 mL | 20 mL | 80 mL |
Connection to dilution factor
For simple dilutions, the dilution factor equals C₁/C₂ and also equals V₂/V₁. A ten-fold dilution has C₁/C₂ = 10 and uses one part stock in ten total parts. For repeated dilution chains, use the serial dilution calculator; for percent concentration recipes, use the percent solution calculator.
If C₂ is larger than C₁, the calculation is not a dilution by adding solvent; it requires concentration, evaporation, or a stronger stock.
Accuracy and laboratory practice
Accurate dilution depends on volumetric technique. Pipette the calculated stock volume into a clean volumetric flask, add solvent below the mark, mix, then top up carefully to the calibration line. Temperature, meniscus reading, pipette calibration, and incomplete mixing can all affect the final concentration. For high-accuracy work, follow institutional methods and calibration guidance from organizations such as NIST and BIPM.
Use calibrated volumetric glassware for standards.
Do not add the calculated solvent volume blindly if volumes are non-additive; top up to V₂ instead.
Mix thoroughly before use or before taking further aliquots.
Record units and significant figures in the lab notebook.
Quick Reference Card
Solution Dilution — Quick Reference
Quick reference • Solution Dilution Calculator
C1V1 = C2V2; V1 = (C2 × V2) / C1; solvent = V2 − V1Valid range: C1, C2, V1, V2 should be positive except the one unknown; for dilution by solvent, C1 ≥ C2 and V2 ≥ V1
Common Values
⚠ Watch Out
- •Do not mix concentration units between C1 and C2.
- •Do not mix volume units between V1 and V2.
- •Final volume V2 means total solution volume, not solvent volume.
- •If V1 is greater than V2, the target is not a simple dilution.
- •For precise work, top up to the volumetric mark rather than assuming perfect volume additivity.
Pro Tips
- →Leave exactly one of C1, V1, C2, or V2 blank to solve that variable.
- →Use dilution factor C1/C2 as a quick check against V2/V1.
- →Choose pipette volumes that are comfortably within the calibrated range.
- →Mix after adding most solvent and again after topping to the final volume.
- →Carry units through the calculation to catch setup errors.
FAQs
What is the C1V1 equals C2V2 dilution equation?
It is a conservation equation for simple dilutions: stock concentration times stock volume equals final concentration times final volume. It assumes the amount of solute transferred remains constant.
How do I calculate the volume of stock solution needed?
Use V1 = (C2 × V2) / C1. For 1 M final solution, 500 mL final volume, and 10 M stock, V1 = (1 × 500) / 10 = 50 mL.
How do I find the volume of solvent to add?
After calculating the stock volume V1, subtract it from the final volume V2: solvent to add = V2 − V1. In practice, add solvent to the final calibration mark rather than relying only on volume additivity.
Can I use millilitres and molarity together?
Yes. C1 and C2 must use the same concentration unit, and V1 and V2 must use the same volume unit. The matching units cancel in the ratio.
What if the final concentration is higher than the stock concentration?
That is not a dilution by adding solvent. The computed V1 may exceed V2, giving a negative solvent volume. You need a more concentrated stock or a concentration step such as evaporation.
Is C1V1 equals C2V2 valid for all mixtures?
It is appropriate for simple dilution of the same solute where the solute amount is conserved. It does not account for chemical reactions, precipitation, density changes in mass-percent preparations, or non-additive mixing volumes.