SDT

Chemistry

Serial Dilution Table Calculator

Generate a stepwise serial-dilution table with concentration, cumulative dilution, transferred moles, and cumulative diluent usage.

Stock molarity (mol/L)Transfer volume per step (mL)Diluent volume per step (mL)Number of dilution stepsAnalytical sample volume (mL)

Volume after each dilution (mL)-

Concentration retained per step-

Molarity after all steps (mol/L)-

Stock divided by final concentration-

Moles in entered final sample (mol)-

Total diluent used (mL)-

Decision view

Serial dilution concentration by step

Serial dilution concentration by stepDilution step is the x-axis; molarity in mol/L is the y-axis on the exact compounded dilution series.

Exact scenario comparisonNumber of dilution steps changes while all other entered assumptions remain constant.

Number of dilution steps	Volume after each dilution (mL)	Concentration retained per step	Molarity after all steps (mol/L)	Stock divided by final concentration	Moles in entered final sample (mol)	Total diluent used (mL)

Period-by-period detail

Complete serial dilution table

Each step compounds the same exact transfer-to-total-volume ratio from the stock solution.

How to use Serial Dilution Table Calculator

Enter stock concentration and repeated volumes.
Choose the step count.
Enter the final sample volume.
Read the logarithmic step chart and complete table.

Calculator guide

Understanding Serial Dilution Table Calculator

A serial dilution compounds the same retained concentration fraction at every step. The final concentration therefore changes exponentially, even though the transfer and diluent volumes stay constant.

One step Transfer and diluent define f.

Compounding f is raised to k.

Table Every tube remains auditable.

Check Stock divided by DF matches final M.

Calculation method

How the calculation works

Build a molarity lab table by applying the same transfer-to-total-volume ratio at every serial dilution step. Divide the transferred volume by total step volume for the retained fraction, raise that fraction to the step number, and multiply by the stock molarity.

Detailed calculation process

Compound a repeated serial dilution one step at a time

The default transfers 10 mL into 90 mL diluent for six steps from a 1 mol/L stock and evaluates a 2 mL final sample.

General formula: V_step = V_t + V_df = V_t/V_stepM_k = M_0 f^kDF_k = 1/f^kn_sample = M_N(V_sample/1000)V_d,total = NV_d Each tube retains fraction f of the previous tube concentration. Repeating the same operation N times multiplies the stock by f to the Nth power.

What each symbol means

V_t, V_d, V_step Transfer, diluent, and total step volumes (mL).

f Concentration fraction retained per step (dimensionless).

M_0, M_k Stock and step-k molarity (mol/L).

k, N Current and final dilution-step counts.

DF_k Cumulative dilution factor relative to stock.

V_sample Final analytical sample volume (mL).

n_sample Moles in the final sample.

V_d,total Total diluent used across all steps (mL).

Worked substitution with the default inputs

1. Calculate one-step volume V_step = 10 + 90 = 100 mL Transferred solution and new diluent form the same total in every tube.

2. Find the retained fraction f = 10/100 = 0.1 Each step retains one tenth of the previous concentration.

3. Compound six steps M_6 = 1(0.1)^6 = 0.000001 mol/LDF_6 = 1/(0.1)^6 = 1,000,000 The sixth tube is one million times more dilute than the stock.

4. Find moles in the sample V_sample = 2/1000 = 0.002 Ln_sample = 0.000001(0.002) = 0.000000002 mol The sample-volume conversion is separate from the serial-dilution volumes.

5. Reconcile diluent usage V_d,total = 6(90) = 540 mLM_0/DF_6 = 1/1,000,000 = 0.000001 mol/L The independent dilution-factor check matches the compounded final concentration.

Six default 1:10 steps produce 1.0×10^-6 mol/L, a cumulative 1,000,000-fold dilution, and 2.0×10^-9 mol in the final 2 mL sample.

Purpose-built visual

Read a logarithmic dilution step chart

Concentration falls by a constant ratio, so a log-scaled vertical axis shows each compounded step without flattening the later values.

Steps Discrete dilution operations.

Log axis Orders of magnitude remain visible.

Markers Exact tube concentrations.

Table Volumes and factors reconcile.

Worked situations

Practical examples

Every default step divides concentration by ten.
Step 3 is 0.001 mol/L.
Step 6 is 0.000001 mol/L.

Better inputs

Useful tips

Mix completely before every transfer.
Use calibrated pipettes.
Keep concentration above the assay detection limit.

Before relying on the result

Limitations and common mistakes

Carryover, mixing error, adsorption, contamination, and pipette uncertainty are excluded.
The transfer ratio is constant at every step.
The table is not a validated laboratory protocol.

Reference

Key terms

Serial dilution: Repeated dilution using material from the preceding step.
Retained fraction: Transfer divided by total step volume.
Dilution factor: Stock concentration divided by diluted concentration.
Log scale: Axis where equal spacing represents equal multiplication.

Important note

Calculated from the entered values using the displayed chemical relationship. Confirm identity, units, purity, conditions, and laboratory safety requirements.

Frequently asked questions

Why is the chart logarithmic?

Repeated dilution spans several orders of magnitude.

Does a 1:10 step mean adding 10 mL to 90 mL?

Yes for these defaults: 10 mL is one tenth of the 100 mL total.

Why compound rather than add factors?

Each step acts on the already diluted preceding tube.

Does the calculator include pipette error?

No. It reports exact arithmetic from entered volumes.