Solution Dilution Calculator (C1V1 = C2V2)
Calculate the volume or concentration needed to dilute a solution using the universal dilution equation. Enter any three values to solve for the fourth.
A general-purpose chemistry and laboratory dilution tool.
Quick examples
The concentration of your original, undiluted solution.
The volume of the concentrated solution you are starting with.
The desired concentration after adding diluent.
Dilution Formula Reference
The Dilution Equation
C1 × V1 = C2 × V2
Solve for Final Volume
V2 = (C1 × V1) ÷ C2
Solve for Final Concentration
C2 = (C1 × V1) ÷ V2
Diluent to Add
Diluent = V2 − V1
C = concentration, V = volume. Subscript 1 = before dilution (starting), subscript 2 = after dilution (final). All units must be consistent.
What Is Dilution?
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent (diluent). The total amount of solute stays the same — only the concentration changes because the volume increases. This is a fundamental concept in chemistry, biology, and laboratory science.
For example, if you have 1 mL of a 10 mg/mL solution and add 9 mL of solvent, you now have 10 mL of a 1 mg/mL solution. The total mass of solute (10 mg) has not changed — it is simply distributed across a larger volume.
The Dilution Formula (C1V1 = C2V2)
The dilution equation is one of the most commonly used formulas in chemistry and laboratory work. It states that the product of concentration and volume before dilution equals the product of concentration and volume after dilution:
Where:
- C1 = starting (initial) concentration
- V1 = starting (initial) volume of the concentrated solution
- C2 = target (final) concentration after dilution
- V2 = total final volume of the diluted solution
This equation works because the total amount of solute is conserved. The mass of solute before dilution (C1 × V1) equals the mass of solute after dilution (C2 × V2). You can rearrange this formula to solve for any one of the four variables, as long as you know the other three.
Worked Example
Suppose you have a solution with a concentration of 5 mg/mL and a volume of 1 mL. You want to dilute it to a target concentration of 2.5 mg/mL. What total volume do you need, and how much diluent should you add?
Given: C1 = 5 mg/mL, V1 = 1 mL, C2 = 2.5 mg/mL
Step 1: V2 = (C1 × V1) ÷ C2
Step 2: V2 = (5 × 1) ÷ 2.5 = 5 ÷ 2.5 = 2 mL
Step 3: Diluent to add = V2 − V1 = 2 − 1 = 1 mL
You need a total final volume of 2 mL. Since you already have 1 mL, add 1 mL of diluent (solvent). The resulting solution will be 2.5 mg/mL.
You can verify the result: 5 mg/mL × 1 mL = 5 mg of solute. 2.5 mg/mL × 2 mL = 5 mg of solute. Both sides equal 5 mg, confirming the calculation is correct.
Serial Dilutions Explained
A serial dilution is a series of sequential dilutions, where each step uses the output of the previous step as the input. This technique is used when a very large dilution factor is needed or when you want to create a range of concentrations from a single stock solution.
For example, a 1:10 serial dilution performed three times yields a final dilution factor of 1:1,000 (10 × 10 × 10 = 1,000). Each step reduces the concentration by 10-fold. This is more practical and more accurate than trying to measure a very small volume of stock solution for a single large dilution.
The C1V1 = C2V2 formula applies to each individual step in a serial dilution. You calculate the volumes for each step separately, using the output concentration of one step as the input concentration for the next.
Common Dilution Mistakes
Understanding these frequent errors will help you avoid them in the laboratory or on exams:
- Confusing total volume with added volume. The formula gives you V2, the total final volume — not the amount of diluent to add. The diluent to add is V2 minus V1. For instance, if V2 = 10 mL and V1 = 2 mL, you add 8 mL of diluent, not 10 mL.
- Unit mismatches. C1 and C2 must be in the same units (e.g., both in mg/mL). V1 and V2 must also be in the same units (e.g., both in mL). Mixing mg/mL with g/L, or mL with uL, will produce incorrect results.
- Trying to concentrate by adding diluent. You cannot increase concentration by adding solvent. If your target concentration is higher than the starting concentration, you need to add more solute, not more solvent. The dilution formula only works when C2 < C1.
- Ignoring the volume of solute. In precise laboratory work, adding a solute may itself change the total volume. The C1V1 = C2V2 formula assumes that the solute volume is negligible or that you are only adding pure solvent (diluent).
- Rounding too early. Keep full precision through intermediate steps and only round the final answer. Premature rounding in serial dilutions can compound errors across multiple steps.
When to Use This Calculator
This dilution calculator is useful for any situation where you need to reduce the concentration of a solution. Common applications include:
- Preparing standard solutions from concentrated stock solutions in a chemistry lab
- Creating calibration curves with known concentrations
- Diluting buffer solutions to working concentrations
- Reducing the concentration of a reagent for an experiment
- Verifying dilution math on homework or exams
- Planning serial dilution series
Frequently Asked Questions
What does C1V1 = C2V2 mean?
C1V1 = C2V2 is the dilution equation. It states that the amount of solute before dilution (concentration times volume) equals the amount of solute after dilution. C1 is the starting concentration, V1 is the starting volume, C2 is the final concentration, and V2 is the final total volume. You can solve for any single unknown if you know the other three values.
What is the difference between total volume and added volume?
Total volume (V2) is the complete volume of the final diluted solution — it includes both the original solution and the diluent you added. Added volume (the diluent) is V2 minus V1. This is one of the most common mistakes in dilution calculations: the formula gives you V2 (total), not the volume of diluent to add. Always subtract V1 from V2 to determine how much diluent is needed.
Can I use this formula with any concentration units?
Yes, as long as C1 and C2 are in the same units. You can use mg/mL, g/L, mol/L (molarity), % w/v, or any other concentration unit. Similarly, V1 and V2 must be in the same volume units (both mL, both L, etc.). The formula is unit-agnostic — it only requires internal consistency.
What is a dilution factor?
The dilution factor is the ratio of the initial concentration to the final concentration (C1 / C2), or equivalently, the ratio of the final volume to the initial volume (V2 / V1). A dilution factor of 10 means the concentration was reduced 10-fold. A "1:10 dilution" means 1 part solution to 9 parts diluent, resulting in 10 parts total and a 10x reduction in concentration.
How do I perform a serial dilution?
To perform a serial dilution, apply the C1V1 = C2V2 formula repeatedly. Start with your stock solution, dilute it to an intermediate concentration, then use that intermediate solution as the starting point for the next dilution. For example, three consecutive 1:10 dilutions produce concentrations of C/10, C/100, and C/1000 from the original stock concentration C. Serial dilutions are more accurate than a single large dilution because they avoid the need to measure very small volumes of concentrated solution.
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