Chemistry calculator
Dilution Calculator
Solve the dilution equation C1 × V1 = C2 × V2 for any concentration or volume, with units converted automatically.
Calculated V2
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Enter the other three values to calculate.
What is a dilution?
A dilution lowers the concentration of a solution by adding solvent while keeping the amount of dissolved solute constant. The dilution calculator finds any one of the four values in the relationship between the starting and ending solutions.
Dilution formula
C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume. Concentrations must have the same dimensions, and volumes must have the same dimensions. This calculator converts them to M and L internally.
How to use C1V1 = C2V2
Choose the value you want to find, enter the other three values, and select each unit. The calculator converts M, mM, and µM to mol/L and µL, mL, and L to liters before rearranging the equation.
For example, 1 M × 100 mL = 0.5 M × V2, so V2 is 200 mL. The volume of solvent to add would be 100 mL if the initial 100 mL is already part of the final solution.
Worked dilution examples
To find a final concentration, use 2 M × 25 mL = C2 × 100 mL, giving C2 = 0.5 M.
For a mixed concentration-unit example, 1 M is 1,000 mM. With C2 = 100 mM and V2 = 500 mL:
Common laboratory dilution uses
Dilutions are used to prepare calibration standards, make working solutions from concentrated stocks, reduce reagent strength, prepare serial dilutions, and bring samples into the measurable range of an instrument. In practice, mix thoroughly and treat V2 as the total final solution volume.
Dilution versus molarity
Molarity calculates concentration from the amount of solute and total solution volume. Dilution calculations compare two concentrations and volumes when the solute amount stays constant. Use the molarity calculator when moles or mass are known; use this calculator when a stock and a final solution are related.
Frequently asked questions
Can I mix mM and M?
Yes. The calculator converts both to mol/L, so 1 M equals 1,000 mM and 1 mM equals 1,000 µM.
Can I mix mL and L?
Yes. µL, mL, and L are converted to liters before the calculation, and the answer is shown in the selected output unit.
What does a zero input mean?
Zero is accepted as a concentration or numerator where the equation remains defined. A zero denominator cannot produce a meaningful result, so the calculator shows a dash until a positive divisor is entered.
What is the difference between V1 and V2?
V1 is the volume of the initial stock solution being used. V2 is the total volume after dilution, including the stock and added solvent.
How the dilution calculator works
A dilution lowers the concentration of a solution by adding solvent while the amount of dissolved solute stays the same. Because the number of moles of solute before and after is identical, concentration multiplied by volume is constant, and that single relationship lets you find any one of the four quantities if you know the other three.
Choose which value to solve for, enter the remaining three, and pick the unit for each field separately. The calculator converts everything to a common base (molar and liters) before solving, then reports the answer back in the unit you selected, so you can mix millimolar with micromolar or microliters with milliliters without converting by hand.
Dilution formula
C1 and V1 are the concentration and volume of the stock you start with; C2 and V2 describe the diluted solution. The most common lab question is how much stock to measure out, which is the V1 form. To make 250 mL of 0.1 M hydrochloric acid from a 2 M stock: V1 = (0.1 M × 250 mL) ÷ 2 M = 12.5 mL. Measure 12.5 mL of stock and add solvent until the total volume reaches 250 mL.
Note that V2 is the final total volume, not the amount of solvent you add. In the example you add about 237.5 mL of water, because the 12.5 mL of stock is part of the final 250 mL.
Units and conversions
The equation works with any concentration unit as long as both sides use the same one, and likewise for volume. The calculator handles the common laboratory units:
- Concentration: M (mol/L), mM (1 mM = 0.001 M), µM (1 µM = 0.000001 M)
- Volume: L, mL (1 mL = 0.001 L), µL (1 µL = 0.000001 L)
- Mixed units are fine: a 10 mM stock diluted to 50 µM in 2 mL needs V1 = (0.05 mM × 2 mL) ÷ 10 mM = 0.01 mL, or 10 µL
Dilution factor and serial dilutions
The dilution factor is the ratio V2 ÷ V1, which equals C1 ÷ C2. A 1:10 dilution means the final volume is ten times the stock volume, so the concentration drops to one tenth. For very large factors it is more accurate to dilute in steps, because measuring 1 µL of stock into a liter is far less precise than performing three successive 1:10 dilutions. Multiply the factors of each step to get the overall dilution: three 1:10 steps give 1:1,000.
When the equation does not apply
C1V1 = C2V2 assumes the solute is simply being spread through more solvent. It does not account for volume change on mixing, which can be noticeable for concentrated acids and alcohols, and it does not model reactions, precipitation, or evaporation. It also assumes you are diluting, so a calculated C2 greater than C1 means a value was entered incorrectly. For safety, always add concentrated acid to water rather than the reverse.
Frequently asked questions
What does C1V1 = C2V2 mean?
It states that the amount of solute is conserved during a dilution: the initial concentration times the initial volume equals the final concentration times the final volume. Knowing any three of the values lets you solve for the fourth.
How do I calculate how much stock solution to use?
Rearrange the equation to V1 = (C2 × V2) ÷ C1. For 500 mL of a 0.5 M solution from a 5 M stock, V1 = (0.5 × 500) ÷ 5 = 50 mL of stock, topped up with solvent to 500 mL.
Is V2 the final volume or the amount of water added?
V2 is the total final volume of the diluted solution. The solvent you add is V2 minus V1.
Can I use different units for C1 and C2?
Yes. The calculator converts M, mM, and µM to a common base before solving, and does the same for L, mL, and µL, so each field can use its own unit.
How do I make a 1:100 dilution?
Combine 1 part stock with 99 parts solvent so the final volume is 100 times the stock volume, for example 10 µL of stock made up to 1 mL. The concentration falls to one hundredth of the original.
Does the dilution equation work for percent concentrations?
Yes, as long as both concentrations are expressed the same way, such as percent weight per volume. The ratio is what matters, not the specific unit.