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Slope: percent, degrees, ratio

A slope between percent, degrees and 1:n ratio, or from rise and distance, with the real road length.

Parameters

Result

Slope

10 % · 5.7106°

Calculation
angle = atan(10 / 100) = 5.7106°
Ratio
1:10
100 m100.5 m10 m5.71°
Ratio
1:10
Rise per 100 m flat
10 m
Road covered per 100 m flat
100.5 m
Note

This slope is 10 %, that is an angle of 5.7106°.

Calculation, assumptions and sources

OverviewA slope in percent, in degrees, as a 1:n ratio (accessibility ramps) and as rise per hundred metres of horizontal distance.

A slope in percent, in degrees, as a 1:n ratio (accessibility ramps) and as rise per hundred metres of horizontal distance. Input of your choice: the percentage, the angle, or the rise and the horizontal distance.

Method & formulasslope (%) = 100 × rise / horizontal distance
slope (%) = 100 × rise / horizontal distanceangle = atan(slope / 100)ratio 1:n with n = 100 / sloperoad = √(distance² + rise²)

The slope in percent is one hundred times the tangent of the angle. The road length comes from Pythagoras.

Slope in percent
the rise per 100 m of horizontal advance. It exceeds 100% beyond 45°.
Ratio 1:n
one metre climbed per n metres advanced, the notation of accessibility standards. 5% = 1:20.
Rise
the altitude difference between two points.
Horizontal distance
the flat distance, the map’s. The road is the hypotenuse, which is longer.
Validity domainExact trigonometry.

Exact trigonometry. If the distance entered is measured along the road (wheel, GPS), the true slope is slightly higher than the rise/distance quotient; the gap stays under 1% up to a 14% slope. Slopes are positive, from 0° included to 90° excluded.

A 100% slopeA 100% slope is 45°: one metre of climb per metre of advance.

A 100% slope is 45°: one metre of climb per metre of advance. The percentage, the tangent of the angle, grows without bound. 200% makes 63°, 1000% makes 84°, and vertical has no percentage. A "60%" shown by a hiking GPS corresponds to 31°.

Reading the resultA 1:20 ramp is the usual accessibility threshold for a path without landings.

A 1:20 ramp is the usual accessibility threshold for a path without landings. Per hundred flat metres, the road measures 100.5 m at 10% and 141 m at 100%.