What is a 1-in-10 serial dilution?

Each step takes 1 part of the previous tube and adds 9 parts diluent, giving a 10× dilution per step. After k steps the total dilution is 10^k.

Why use serial dilutions instead of one big dilution?

To dilute by 10⁶ in a single step you'd need a 1 μL sample in a litre of diluent, which is impractical and inaccurate. Six 1:10 steps each move 100 μL into 900 μL, which is reliable.

What's the formula for the kth tube?

Cₖ = C₀ / d^k. The concentration in tube k is the original concentration divided by the dilution factor raised to k.

Does this account for the diluent volume?

It computes the concentration ratio only. For total volume you separately track how much you transfer (e.g. 100 μL into 900 μL diluent for 1:10).

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NSW · HSCBiology

Serial dilution factor

Get every tube concentration in a k-step serial dilution. Useful for plating bacteria, antibody titres, or any stepwise dilution series.

Formula

Cₖ = C₀ / d^k

Total dilution after k steps: D = d^k.

Inputs

Initial concentration C₀Concentration unitCosmetic only. Examples: M, mg/mL, CFU/mL.Dilution factor d (per step)A 1-in-10 dilution has d = 10.Number of serial steps kNumber of times the dilution is applied in series.

Serial dilution: Cₖ = C₀ / d^k. Total dilution = d^k.

Result

Final tube concentration

0.00001000 M

Overall dilution = 100,000× (1 in 100,000).

Per-tube concentrations

Tube	Concentration (M)	Dilution
#0	1.000	1×
#1	0.1000	10×
#2	0.01000	100×
#3	0.001000	1,000×
#4	0.0001000	10,000×
#5	0.00001000	100,000×

Worked example

A stock solution at C₀ = 1 M is diluted 1:10 (d = 10) five times in series. The concentration in each tube:

Tube 0: 1 M (1× dilution)
Tube 1: 0.1 M (10×)
Tube 2: 0.01 M (100×)
Tube 3: 0.001 M (1000×)
Tube 4: 1 × 10⁻⁴ M (10 000×)
Tube 5: 1 × 10⁻⁵ M (100 000×)

Overall dilution = 10⁵ = 100 000×. Final concentration C₅ = 1 / 10⁵ = 1 × 10⁻⁵ M.

How this calculator works

For each step i from 0 to k the calculator outputs C₀ / d^i. The total overall dilution after k steps is d^k. The unit is purely cosmetic; the maths is unit-independent.

Common questions

What is a 1-in-10 serial dilution?: Each step takes 1 part of the previous tube and adds 9 parts diluent, giving a 10× dilution per step. After k steps the total dilution is 10^k.
Why use serial dilutions instead of one big dilution?: To dilute by 10⁶ in a single step you'd need a 1 μL sample in a litre of diluent, which is impractical and inaccurate. Six 1:10 steps each move 100 μL into 900 μL, which is reliable.
What's the formula for the kth tube?: Cₖ = C₀ / d^k. The concentration in tube k is the original concentration divided by the dilution factor raised to k.
Does this account for the diluent volume?: It computes the concentration ratio only. For total volume you separately track how much you transfer (e.g. 100 μL into 900 μL diluent for 1:10).