THE NUMBERS, EXPLAINED
How to use this calculator.
Grade is rise divided by horizontal run; belt distance is along the slope. This is geometric equivalent gain.
Start with your inputs
Enter belt distance (km), grade (%). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Belt distance (km) | 5 |
| Grade (%) | 10 |
A worked example
With the example inputs above, approximate vertical gain (m) is 497.518595. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Approximate vertical gain (m)
(5) × 1000 × ((10) ÷ 100) ÷ sqrt(1+((10) ÷ 100)^2) = 497.518595
| Result | Example answer |
|---|---|
| Approximate vertical gain (m) | 497.518595 |
How this is calculated
Approximate vertical gain (m)
a × 1000 × (b ÷ 100) ÷ sqrt(1+(b ÷ 100)^2)
Symbols and units
- a
- Belt distance (km)
- b
- Grade (%)
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
sqrt(x) is the non-negative square root of x.
Assumptions and limits
Grade is rise divided by horizontal run; belt distance is along the slope. This is geometric equivalent gain.
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?
Approximate vertical gain (m). 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: Grade is rise divided by horizontal run; belt distance is along the slope. This is geometric equivalent gain.
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.
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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