Dilution Calculator

1. Pick which variable to solve for. The most common case is solving for V1 (how much stock to take) when you know the desired final concentration and volume.
2. Select your units. Concentration units like %, M (molar), or g/L. Volume units like mL, L, or fluid ounces. Use the same unit on both sides of the equation.
3. Enter the three known values. The calculator solves the unknown using C1·V1 = C2·V2.
4. Follow the procedure: measure out the stock volume, then add solvent up to the final volume — not to the stock. The final volume is your target, not the volume of solvent added.

Every dilution problem reduces to a single equation: the amount of solute before dilution equals the amount of solute after dilution.

C1 × V1 = C2 × V2

Where:
C1 = stock (starting) concentration
V1 = volume of stock used
C2 = final (target) concentration
V2 = final total volume

Example: Make 100 mL of 1% bleach solution from 8.25% household bleach.

• C1 = 8.25%, V1 = ?, C2 = 1%, V2 = 100 mL
• V1 = (C2 × V2) / C1 = (1 × 100) / 8.25 = 12.12 mL of bleach
• Add to the bleach: 100 − 12.12 = 87.88 mL of water

When the target concentration is more than 100× weaker than the stock, a single-step dilution becomes hard to measure accurately. To make a 1 nM solution from a 1 M stock, you'd need to pipette 1 µL into 1 L of solvent — and 1 µL pipettes have ±5-10% error at low volumes, which compounds badly.

The solution: serial dilution. Make the dilution in stages, each step diluting by a manageable factor (typically 10× or 100×):

Step 1: 1 M → 0.01 M  (1:100, 100 µL stock + 9.9 mL solvent)
Step 2: 0.01 M → 0.0001 M  (1:100, 100 µL of step 1 + 9.9 mL)
Step 3: 0.0001 M → 1 nM  (1:100, 100 µL of step 2 + 9.9 mL)

Three rules to follow for accuracy:

• Vortex/mix thoroughly after each step. An unmixed dilution silently breaks subsequent steps.
• Use fresh pipette tips at every step to avoid carry-over contamination, especially with detergents or sticky compounds.
• Don't exceed 1:1000 in a single step. The error stacking gets unacceptable. Stay at 1:100 or smaller per step.

This calculator handles single-step dilutions. For serial dilutions, run the calculator multiple times — set V2 to your step volume (usually 10 mL), and chain the C2 of each step as the C1 of the next.