THE NUMBERS, EXPLAINED
How to use this calculator.
Steady repeating service with equal headway in both directions; cycle includes both runs and terminal recoveries. Spare vehicles and driver constraints are excluded.
Start with your inputs
Enter outbound running time (min), inbound running time (min), recovery at first terminal (min), recovery at second terminal (min), target headway (min). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Outbound running time (min) | 40 |
| Inbound running time (min) | 35 |
| Recovery at first terminal (min) | 10 |
| Recovery at second terminal (min) | 5 |
| Target headway (min) | 15 |
A worked example
With the example inputs above, round-trip cycle (min) is 90. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Round-trip cycle (min) | 90 |
| Minimum scheduled buses | 6 |
| Extra cycle time from whole-bus rounding (min) | 0 |
How this is calculated
Round-trip cycle (min)
Add both running times and both terminal recoveries.
Minimum scheduled buses
Divide cycle time by headway and round up.
Extra cycle time from whole-bus rounding (min)
Subtract required cycle from buses times headway.
Symbols and units
- a
- Outbound running time (min)
- b
- Inbound running time (min)
- c
- Recovery at first terminal (min)
- d
- Recovery at second terminal (min)
- e
- Target headway (min)
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
Steady repeating service with equal headway in both directions; cycle includes both runs and terminal recoveries. Spare vehicles and driver constraints are excluded.
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?
Round-trip cycle (min); Minimum scheduled buses; Extra cycle time from whole-bus rounding (min). 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: Steady repeating service with equal headway in both directions; cycle includes both runs and terminal recoveries. Spare vehicles and driver constraints are excluded.
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.
Read the quality report →