THE NUMBERS, EXPLAINED
How to use this calculator.
Enter people in the same order in both lists. Total paid must equal total owed. This returns a valid settlement, not necessarily every possible solution.
Start with your inputs
Enter amounts paid (£), amounts owed (£). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Amounts paid (£) | 60,0,0 |
| Amounts owed (£) | 20,20,20 |
A worked example
With the example inputs above, settlement transfers is Person 2 → Person 1: £20.00; Person 3 → Person 1: £20.00. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Settlement transfers | Person 2 → Person 1: £20.00; Person 3 → Person 1: £20.00 |
How this is calculated
Settlement transfers
settlement(a,b)
Symbols and units
- a
- Amounts paid (£)
- b
- Amounts owed (£)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
For each person, subtract owed from paid and round to pennies. In input order, transfer money from a person with a negative balance to one with a positive balance, until both sides are settled. Reject a residual rounding mismatch. This does not minimise the number of transfers.
Assumptions and limits
Enter people in the same order in both lists. Total paid must equal total owed. This returns a valid settlement, not necessarily every possible solution.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Settlement transfers. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Enter people in the same order in both lists. Total paid must equal total owed. This returns a valid settlement, not necessarily every possible solution.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →