Dilution calculator (C₁V₁ = C₂V₂)
Solve C₁V₁ = C₂V₂ for the stock volume or final concentration, get the diluent to add, and plan serial dilutions with the concentration after every step.
Your solutions
Any concentration unit works (M, mM, mg/mL, %, ×) as long as C₁ and C₂ share it; volumes are in mL. The equation assumes volumes add and the solute is conserved. In the lab, add the stock first, then diluent up to the final volume.
How the calculation works
Dilution calculator (C₁V₁ = C₂V₂): common questions
Wondering about the why? Start here.
How do you use C1V1 = C2V2?
C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and volume you want to end up with. Rearrange for the unknown: to make 100 mL of 1 M from a 10 M stock, V₁ = C₂V₂ / C₁ = 1 × 100 / 10 = 10 mL of stock, then add 90 mL of water to reach 100 mL. Any concentration unit works (M, mM, mg/mL, %, ×) as long as C₁ and C₂ share it.
Read: lab measurements and scaleWhat is a serial dilution?
A serial dilution repeats the same dilution factor step after step, each tube made from the previous one. Three 1 : 10 steps from a 10 M stock give 1 M, 0.1 M, and 0.01 M, a total dilution of 1,000×; each step transfers 1 part into 9 parts of diluent. Serial dilutions are how you count bacteria on plates, build a standard curve, or find the lowest antibiotic dose that stops growth.
Count the bacteria you diluteWhat is the dilution factor?
The dilution factor is the final volume divided by the stock volume, V₂ / V₁, which equals C₁ / C₂. Taking 10 mL of stock up to 100 mL is a 10× or 1 : 10 dilution. For 500 mL of 70% ethanol from 95%, V₁ = 70 × 500 / 95 = 368.4 mL of stock plus 131.6 mL of water, a dilution factor of about 1.36×.
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