THE NUMBERS, EXPLAINED
How to use this calculator.
One account, no pending transactions; all crossings charged exactly as entered. Top-up timing is the first crossing index whose cumulative cost exceeds available balance.
Start with your inputs
Enter planned crossing charges in chronological order, current toll account balance, required ending balance. Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Planned crossing charges in chronological order | 5,10,5 |
| Current toll account balance | 12 |
| Required ending balance | 5 |
A worked example
With the example inputs above, total planned toll charges is 20. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Total planned toll charges | 20 |
| Required top-up | 13 |
| First crossing requiring top-up | 2 |
How this is calculated
Total planned toll charges
Sum supplied crossing charges.
Required top-up
Add desired ending balance to charges and subtract current balance.
First crossing requiring top-up
Find the first cumulative charge above current balance; zero means none.
Symbols and units
- a
- Planned crossing charges in chronological order
- b
- Current toll account balance
- c
- Required ending balance
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
One account, no pending transactions; all crossings charged exactly as entered. Top-up timing is the first crossing index whose cumulative cost exceeds available balance.
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?
Total planned toll charges; Required top-up; First crossing requiring top-up. 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: One account, no pending transactions; all crossings charged exactly as entered. Top-up timing is the first crossing index whose cumulative cost exceeds available balance.
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
OpenStax: Solve proportions and their applications ↗
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.
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