All calculatorsSerial Dilution Calculator
Generate a serial dilution series from a stock solution. Enter the initial concentration C₀, the dilution per step (as a factor, a 1:x ratio, or transfer/total volumes), and the number of steps. See step-by-step math, a results table, and visuals (decay curve + final-concentration gauge).
Background
For an equal-step series, each step multiplies the concentration by the same dilution factor D (e.g., 0.1 for a 10× dilution). The concentration after step n is Cn = C0 × Dn. Common inputs:
- Factor D (0 < D < 1), e.g., D = 0.1 for 10× dilution
- Ratio 1:x, where D = 1/x (e.g., 1:3 → D = 1/3)
- Transfer/Total, where D = Vtransfer / Vfinal
How to use this calculator
- Enter C₀ and unit (label only).
- Choose a dilution mode: factor D, ratio 1:x, or transfer/final.
- Set the number of steps. We compute Cn = C0 × Dn for each step.
- Toggle sig-fig and scientific notation for readable outputs.
Formula & Equation Used
Serial dilution: Cn = C0 × Dn
Factor: D ∈ (0,1). Example: 10× dilution → D = 0.1
Ratio: 1:x → D = 1/x
Transfer/Final: D = Vtransfer / Vfinal
Example Problems & Step-by-Step Solutions
Example 1 — 1.00 M stock, 10× per step, 5 steps
D = 0.1 → C₅ = 1.00 × 0.1⁵ = 1.0×10⁻⁵ M.
Example 2 — 10 mg/mL, D = 0.5, 4 steps
C₄ = 10 × 0.5⁴ = 10 × 1/16 = 0.625 mg/mL.
Example 3 — 5.0% (1:5 per step), 3 steps
D = 1/5 → C₃ = 5.0 × (1/5)³ = 5.0/125 = 0.040%.
Frequently Asked Questions
Q: What’s the difference between a dilution factor and a “× times” phrase?
“10× dilution” means the solution is 10 times less concentrated per step, so D = 1/10 = 0.1.
Q: Do the units matter?
Units are labels only; the calculator doesn’t convert units. Keep the same unit across steps.
Q: Can I list actual volumes to prepare each tube?
Use the transfer/final mode to compute D from volumes. We keep the series equal-step; you can choose volumes that implement the same D each time.
