Tecnobosque · Terrain and wildfire data
A slope value is incomplete without its units. This guide shows how to distinguish percent slope from degrees, convert between them and check the distance used in a terrain calculation.
Published 20 October 2026 · Educational geometry · Worked examples are hypothetical.
Percent slope and degrees describe the same incline differently
NWCG’s slope lesson distinguishes the rise/run ratio from an angular measurement. The USGS explanation also specifies that the denominator is horizontal distance, not distance along the inclined ground.
- Percent slope: 100 × vertical rise ÷ horizontal run.
- Angle in degrees: arctan(percent slope ÷ 100), with the result expressed in degrees.
- Degrees to percent: 100 × tan(angle), with the input interpreted in degrees.
Use matching length units for rise and run. Metres divided by metres and feet divided by feet produce the same dimensionless ratio. Metres divided by feet without conversion do not.
Slope percentage to degrees: conversion table
| Percent slope | Angle | Equivalent rise |
|---|---|---|
| 0% | 0.00° | 0 m per 100 m horizontal |
| 5% | 2.86° | 5 m per 100 m horizontal |
| 10% | 5.71° | 10 m per 100 m horizontal |
| 20% | 11.31° | 20 m per 100 m horizontal |
| 30% | 16.70° | 30 m per 100 m horizontal |
| 40% | 21.80° | 40 m per 100 m horizontal |
| 50% | 26.57° | 50 m per 100 m horizontal |
| 75% | 36.87° | 75 m per 100 m horizontal |
| 100% | 45.00° | 100 m per 100 m horizontal |
| 150% | 56.31° | 150 m per 100 m horizontal |
| 200% | 63.43° | 200 m per 100 m horizontal |
Values above 100% are possible because rise can exceed horizontal run. For example, 200% means two units of rise per one unit of horizontal run; its angle is about 63.43°. At a vertical face the horizontal run is zero, so this finite rise/run calculation is undefined.
Worked example: read a terrain profile correctly
Suppose two points on a hypothetical profile differ in elevation by 36 metres, with 120 metres of horizontal separation. The average grade between those points is 100 × 36 ÷ 120 = 30%. Its angle is arctan(0.30) ≈ 16.70°.
If a form requests degrees, enter approximately 16.70. If it requests percent, enter 30. If it requests a decimal rise/run ratio, enter 0.30. These are three representations of the same calculation, not three different hills.
A single value between endpoints does not describe every intermediate segment. A profile containing a steep section and a flatter section can have the same endpoint-average grade as a uniform incline. Record the distance and locations that the value represents rather than treating it as a local measurement everywhere along the line.
The ground-distance trap
Consider another idealized straight slope with a 30-metre rise and a 40-metre horizontal run. Its inclined length is 50 metres by the Pythagorean theorem. The correct percent slope is 75%: 100 × 30 ÷ 40.
Dividing the rise by the inclined length instead gives 60%. That arithmetic uses a different denominator and does not produce percent slope. When a distance source says only “distance,” establish whether it is horizontal separation, inclined distance or route length before using it.
The 30–40–50 example assumes a straight planar incline. Do not apply that simple triangle to an uneven walking route and assume it reconstructs the terrain.
A unit check before using a wildfire model or GIS layer
- Read the field definition. Look for percent, degrees or a decimal ratio. A field called “slope” alone is insufficient.
- Keep the original value. Store the source value and unit alongside any converted value. This makes an input error easier to trace.
- Check the calculation mode. A calculator using radians will not interpret a degree input correctly unless you convert it.
- Identify the spatial meaning. Record whether the number describes a profile between two points, a local terrain estimate or a summary over an area.
- Test a known conversion. A correct degree-to-percent setup should return 100% for 45°. Use this as an arithmetic check, not as validation of the underlying terrain data.
For example, treating a documented 30° angle as 30% would substitute 0.30 for the correct rise/run ratio of about 0.5774. That is a substantial input mismatch. Its effect on a model’s output depends on that model; it is not legitimate to turn the input difference into a universal percentage error in fire spread.
What this conversion does not establish
Converting units does not predict fire arrival, determine an evacuation route or validate a terrain dataset. It does not establish a universal rule that a fire moves a fixed multiple faster for each increase in slope. Keep geometry, observations and model results separate.
Continue with the wildfire field guides for terminology and the tools and calculators for individual model assumptions. For interpreting mapped fire effects, see how to read burn severity maps.