Serial Dilution Calculator
Compute concentration at each step of a serial dilution.
Factor of 2 means each step is half the concentration (1:2). Factor of 10 means 1:10.
If provided, calculates transfer and diluent volumes per step.
Formula: Cₙ = C₀ / factorⁿ
Learn more
What it does
The Serial Dilution Calculator lays out a stepwise dilution series and, if a working volume is supplied, the volumes to pipette at every step. Enter the starting concentration, the dilution factor, the number of steps, and optionally the final volume per tube, and it returns the concentration at each step along with the cumulative dilution fold and the sample and diluent volumes. Step 0 is the undiluted stock, so a six-step series produces seven rows. It is the standard way to build a standard curve for ELISA, qPCR, a protein assay or any plate-based readout, and the whole table can be copied or exported as CSV for a worksheet.
How it works
Each step divides the concentration by the dilution factor, so the concentration after i transfers is the starting concentration divided by the factor raised to the power i. The factor describes the fold change in concentration, not the ratio of sample to diluent: a 1:10 dilution means one part sample to nine parts diluent and corresponds to a factor of 10. Two derived quantities make the scheme usable at the bench. The sample volume is the working volume divided by the factor, which for a 1000 microlitre final volume at a factor of 10 is 100 microlitres taken from the previous tube. The diluent volume is the working volume minus that sample volume, here 900 microlitres, so the two always sum back to the working volume. Because the table includes step 0, the undiluted stock, n transfers are listed as n plus one concentrations.
Worked example
Start with a 1.000 mg/mL standard and dilute it tenfold through six steps at a working volume of 1000 microlitres. The series runs 1.000, 0.1000, 0.0100, 0.0010, 1.0000e-4, 1.0000e-5 and 1.0000e-6 mg/mL across seven rows, and every transfer is 100 microlitres of the previous dilution into 900 microlitres of diluent. That range from one to a millionth of a milligram per millilitre spans the working range of a typical protein or antibody standard curve. Change the factor to 100 and the same 1000 microlitre working volume asks for only 10 microlitres of sample per step, so the concentrations fall a hundredfold each time and four steps already reach 1.0000e-8 mg/mL. The pipetting error of a 10 microlitre transfer is proportionally much larger, and because each step inherits the mistakes of the one before it, that error compounds down the series. Doubling the working volume to 2000 microlitres would bring the sample volume back to a comfortable 20 microlitres without changing the concentrations at all.
When to use it
Use it to lay out a dilution series before touching a pipette, to check the volumes a written protocol implies, and to see how quickly a chosen factor runs past the measurable range of the assay. Three practical traps are worth attention. The meaning of the factor is the most common source of error, because many protocols write 1:10 and mean one part sample plus ten parts diluent, a factor of 11 rather than 10. The tool interprets the number as the fold change in concentration, so a factor of 11 entered for a series that is intended to be 1:10 will be more than a full step low in concentration by the fifth row. The second is pipetting precision: below roughly 10 microlitres by hand both accuracy and precision degrade, and a serial dilution multiplies every step error, so a 2 percent error per transfer becomes about 10 percent after five steps, since 1.02 raised to the fifth power is 1.104. The third is that the first row is the undiluted stock and not the first dilution, so reading it as step 1 shifts the whole series and leaves the curve one point short. The tool flags two input problems before computing anything, a factor of exactly 1 and a step count beyond 50, but it cannot resolve the 1:10 ambiguity for you and it does not check whether the final concentrations have fallen below the detection limit of the assay they are intended for.
FAQ
- What does dilution factor mean?
- It is the factor by which the concentration falls, so the concentration after i steps is the starting concentration divided by the factor raised to i. A 1:10 dilution means one part sample plus nine parts diluent and has a factor of 10; a 1:2 dilution is one plus one, a factor of 2. Watch for protocols that write 1:10 but mean one part sample plus ten parts diluent, which is really a factor of 11 and will drift a full step low by the fifth row.
- How do I work out the volumes for each step?
- Decide a working volume, then pipette that volume divided by the factor from the previous dilution, and add diluent to reach the working volume. At 1000 µL and a factor of 10 that is 100 µL of sample into 900 µL of diluent. The tool provides a column for each volume; leave the field blank if only the concentration series is needed.
- Why does the table start at step 0?
- Because the undiluted stock is the first concentration in the series and the reference the others are built from. With n transfers the table holds n + 1 rows: a six-step dilution from 1.000 mg/mL covers 1.000 down to 1.0000e-6 mg/mL in seven rows. Treating row 0 as the first dilution would leave the curve one point short.
- How accurate is a serial dilution?
- The concentrations are exact given perfect pipetting; the error comes from the transfers and accumulates. Each step inherits the error of the one before it, so a 2 percent error per transfer becomes roughly 10 percent after five steps, since 1.02 raised to the fifth power is 1.104. Keep sample volumes above about 10 µL, use fresh tips, and consider an independent dilution from the stock rather than chaining more than six or seven steps.