Dilution math reduces concentration by adding solvent. The fundamental equation is C₁V₁ = C₂V₂ — moles of solute don't change when you dilute, so initial concentration × initial volume equals final concentration × final volume. The Toolenza calculator solves for any one variable given the other three.

When to dilute

• Cost. Concentrated stock takes less storage and ships cheaper. Many lab reagents come at 10× or 100× working concentration to be diluted before use.
• Stability. Some reagents are more stable concentrated and degrade once diluted — make the working solution fresh.
• Safety. Concentrated acids are corrosive; you dilute to a safer working concentration.
• Cell culture. Antibody stocks are typically diluted 1,000–10,000× for staining; pipetting nanolitres directly is unreliable.

Worked examples

• Diluting a 1 M stock to 0.1 M. Want 100 mL final. V₁ = (0.1 × 100) ÷ 1 = 10 mL of stock. Add 90 mL of solvent to reach 100 mL total.
• "1:10 dilution." Add 1 part stock to 9 parts solvent — final concentration is 1/10 of stock. Note: "1:10" means a 1-in-10 ratio, not "1 plus 10" (which would be a 1/11 dilution). The distinction trips up new lab workers regularly.
• Serial dilution. A 1:10 dilution repeated 6 times = 10⁶-fold dilution. Useful when you need very low concentrations without measuring sub-microlitre volumes.

Pitfalls

• Volume isn't additive for concentrated solutions. Adding 50 mL of 95% ethanol to 50 mL of water does NOT give 100 mL — the mixture shrinks slightly due to molecular packing. For precision work, dilute to a final volume in a volumetric flask, not by adding fixed solvent.
• Always add acid to water, not water to acid. The heat of dilution can boil concentrated acid solutions; adding water last lets heat dissipate as it forms.
• Pipette small volumes carefully. A 10× dilution by pipetting 100 µL into 900 µL is accurate; pipetting 1 µL into 9 µL is not (positive-displacement pipettes are needed at that scale).