Dilution Calculator
Dilution is the process of reducing a solution's concentration by adding more solvent, and the fundamental relationship C₁V₁ = C₂V₂ ensures that the total moles of solute are conserved throughout. This calculator solves for the volume of concentrated stock solution required and tells you exactly how much water to add to reach the desired final concentration and volume.
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Formula
C₁V₁ = C₂V₂ → V₁ = C₂V₂ / C₁
C₁ is the concentration of the stock solution. V₁ is the volume of stock solution you will take. C₂ is the desired final concentration. V₂ is the desired final volume. The product C × V gives the total moles of solute, which must be the same before and after dilution — you are only adding solvent. Solving for V₁ gives the volume of stock to pipette, and the difference V₂ − V₁ is how much solvent to add.
How to use the Dilution Calculator
- 1
Enter your stock concentration (c₁)
Value should be in M.
- 2
Enter your final concentration (c₂)
Value should be in M.
- 3
Enter your final volume (v₂)
Value should be in L.
- 4
Read your results instantly
Results update in real time as you type.
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The conservation principle behind C₁V₁ = C₂V₂
When you dilute a solution, you add solvent but no additional solute. The total amount of solute (in moles) therefore remains constant: moles before = moles after. Since moles = M × V, the equation M₁V₁ = M₂V₂ follows directly. This simple relationship allows you to plan any dilution without knowing the identity of the solute — only the concentrations and volumes matter. It applies equally to mass-based concentrations (g/L) and percentage concentrations if you use consistent units throughout. In clinical and pharmaceutical laboratories, this equation is used hundreds of times per day to prepare working reagents from concentrated stocks.
Safe dilution technique in the laboratory
When diluting concentrated acids, always add acid to water, never water to acid. Concentrated sulfuric acid, for example, releases so much heat when mixed with water that adding water to concentrated acid can cause violent boiling and spattering. The mnemonic 'AAA — Add Acid to wAter' can prevent serious injuries. For most non-hazardous solutions, measure the required volume of stock with a calibrated pipette, transfer it to a volumetric flask, and then add solvent up to the graduation mark while mixing periodically. This ensures the final volume is accurate rather than simply adding a measured volume of solvent to the stock.
Tips & Insights
C₂ must be less than C₁ for a dilution
If C₂ is larger than C₁, you are describing a concentration increase, not a dilution, and V₁ would exceed V₂ — a physically impossible result. Check that your final concentration is lower than your stock concentration.
Convert mL to L for consistency
This calculator uses liters. If your volumes are in mL, divide by 1000 before entering. You can also work entirely in mL as long as all volume inputs use the same unit.
Prepare dilutions in a volumetric flask
Always make your final volume up to the mark in a calibrated volumetric flask rather than adding a fixed volume of water. This accounts for the volume change that occurs when concentrated solutions are diluted.
Worked Examples
Preparing 1 M HCl from 12 M stock
Add 41.67 mL of stock to a flask and dilute to 500 mL total — a 12-fold dilution.
Lab reagent preparation
Take 10 mL of 10 M stock and dilute to 1 L with water for a 100-fold dilution to 0.1 M.
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Frequently Asked Questions
Can I use C₁V₁ = C₂V₂ for any unit of concentration?
Yes, as long as you use the same concentration unit on both sides (M, g/L, %, etc.) and the same volume unit on both sides. The equation is unit-agnostic as long as you are consistent.
What if I need to dilute by a specific factor?
A dilution factor of 1:10 means the final concentration is 1/10 of the original. Set C₂ = C₁/10 and enter your desired final volume. The calculator will tell you to take 1/10 of V₂ from the stock.
Does temperature matter for dilutions?
For high-precision work, yes. Volume depends on temperature, so allow solutions to equilibrate to room temperature before making the final volume adjustment in a volumetric flask.
How do I prepare serial dilutions?
Apply C₁V₁ = C₂V₂ sequentially: dilute the stock to an intermediate concentration, then dilute that to the next lower concentration. Each step uses the output of the previous step as the new C₁.
Why should I add acid to water instead of the reverse?
Concentrated acids release significant heat on dilution. Adding acid slowly to water distributes this heat into the larger water mass, preventing dangerous localized boiling. Reversing the order concentrates the heat in a small volume of water, causing spattering.
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