Dilution Calculator (C1V1 = C2V2)
Enter any 3 values and choose the one you want to calculate. Use consistent units for concentrations and volumes.
What is a dilution calcul?
A dilution calcul is simply the math used to reduce the concentration of a solution by adding solvent (usually water or buffer). It is one of the most common calculations in chemistry, biology, medicine, food science, and even household mixing tasks.
The core idea is this: the amount of solute stays the same before and after dilution. You are not removing material; you are spreading it into a larger volume.
The core formula: C1 × V1 = C2 × V2
The standard dilution equation is:
C1 × V1 = C2 × V2
- C1 = initial (stock) concentration
- V1 = volume taken from stock
- C2 = desired final concentration
- V2 = final total volume after dilution
If you know any three of these values, you can calculate the fourth. That is exactly what the calculator above does.
How to use the calculator
- Choose which variable you want to solve for (C1, C2, V1, or V2).
- Enter the other three known values.
- Click Calculate.
- Read the result and the mixing guidance (stock + diluent).
Tip: Keep units consistent. For example, if concentration is in mg/mL for C1, keep C2 in mg/mL too. If volume is in mL for V1, use mL for V2.
Worked examples
Example 1: Prepare 100 mL of 0.1 M from 1.0 M stock
You know C1 = 1.0 M, C2 = 0.1 M, V2 = 100 mL. Solve for V1.
V1 = (C2 × V2) / C1 = (0.1 × 100) / 1.0 = 10 mL.
So you take 10 mL of stock and add solvent up to 100 mL total volume (which means 90 mL diluent).
Example 2: Dilute bleach from 5% to 0.5% for cleaning
You know C1 = 5%, C2 = 0.5%, and want V2 = 1000 mL. Solve for V1:
V1 = (0.5 × 1000) / 5 = 100 mL.
Mix 100 mL bleach with 900 mL water to make 1 liter of 0.5% solution.
Example 3: Find final concentration after mixing
If C1 = 20 mg/mL and you mix V1 = 2 mL into a final volume V2 = 50 mL:
C2 = (C1 × V1) / V2 = (20 × 2) / 50 = 0.8 mg/mL.
Quick reference table
| Want to solve | Rearranged formula |
|---|---|
| Stock concentration (C1) | C1 = (C2 × V2) / V1 |
| Final concentration (C2) | C2 = (C1 × V1) / V2 |
| Stock volume (V1) | V1 = (C2 × V2) / C1 |
| Final volume (V2) | V2 = (C1 × V1) / C2 |
Serial dilution basics
For very low concentrations, labs often use serial dilution instead of one huge dilution step. A common pattern is repeated 1:10 dilutions:
- Tube 1: stock diluted 1:10
- Tube 2: tube 1 diluted 1:10 again (total 1:100)
- Tube 3: tube 2 diluted 1:10 again (total 1:1000)
This method improves pipetting accuracy and reduces error when target concentrations are extremely small.
Common dilution mistakes (and how to avoid them)
- Mixing units: mL and L in the same calculation without conversion.
- Using concentration by mass and molarity interchangeably: always keep concentration types consistent.
- Confusing final volume with added solvent: V2 is total final volume, not just the solvent volume.
- Rounding too early: keep extra decimals during calculation, round at the end.
- Ignoring safety: concentrated acids/bases need proper PPE and correct mixing order.
FAQ
Can I use any units?
Yes, as long as units are consistent within each variable type. Concentrations must match each other, and volumes must match each other.
What if C2 is larger than C1?
That is not a dilution; it is concentration. The calculator will still compute mathematically, but your process would require removing solvent or using a stronger stock.
How do I calculate diluent volume directly?
Once you have V1 and V2, use: Diluent volume = V2 − V1.
Final thoughts
A reliable dilution calcul workflow saves time, reduces waste, and improves accuracy in both lab and practical settings. Use the calculator above whenever you need quick and consistent results, and double-check units before mixing.