Steeps › How gradients are measured: percent, 1-in-x and degrees
How gradients are measured: percent, 1-in-x and degrees
A road gradient can be written as a percentage, a ratio or an angle. They all describe the same slope, and a few simple sums convert between them.
Three ways to say the same thing
A percentage is the rise divided by the horizontal distance, times 100. A road that rises 1 metre over 4 metres of flat ground is 25%. A ratio such as "1 in 4" says the same thing, written the old British way: it rises 1 for every 4 along. An angle is the slope in degrees.
Conversion table
| Ratio | Percent | Angle (approx.) | Example |
|---|---|---|---|
| 1 in 14 | 7% | 4.1 degrees | Porlock toll road |
| 1 in 5 | 20% | 11.3 degrees | Bealach na Bà maximum |
| 1 in 4 | 25% | 14.0 degrees | Porlock Hill |
| 1 in 3.5 | 28.6% | 16.0 degrees | Ffordd Pen Llech (Guinness) |
| 1 in 3 | 33% | 18.4 degrees | Hardknott, Rosedale |
| 1 in 2.73 | 36.6% | 20.1 degrees | Ffordd Pen Llech (tangent) |
Our calculation: percent equals 100 divided by the second number; the angle is the inverse tangent of the percent divided by 100. A 100% gradient is 45 degrees, not 90, which surprises people.
Why published figures differ
Different surveys measure different things:
- Which stretch. The steepest 10 metres is a different number from the average over the whole road. Rosedale Chimney averages 13% but peaks at 1 in 3.
- Which line. Guinness World Records now measures along the centreline of the street. A measurement taken on a different line, such as the steepest edge of the road, can give a different number.
- Which axis. Wikipedia's list notes that Baldwin Street in Dunedin is 1:3.41 or 16.33 degrees (29.3%) averaged over 161 metres, a different figure from Guinness's 34.8% centreline measurement for the steepest part.
- Rounding for signs. UK practice rounds up, so the Ffordd Pen Llech sign shows 40% for a 36.6% tangent gradient.
Slope length or horizontal length?
Strictly, a percentage uses the horizontal distance, not the distance along the road surface. On gentle slopes the difference is tiny; on a 1 in 3 slope the surface distance is about 5% longer than the horizontal distance. Different tools, such as GPS cycle computers, can report slightly different numbers for the same road.
Using the numbers
For cycling, the maximum matters for whether you can ride it; the average tells you how long the effort lasts. For driving, a 1 in 3 slope means a heavy vehicle may struggle to climb. See cycling climbs, driving steep hills, and the record dispute that came from these differences.
A worked example
Take Porlock Hill, with a steepest section near 1 in 4. For every 4 metres you travel across the ground, you rise 1 metre. That is 100 divided by 4, or 25%. The angle is the inverse tangent of 0.25, about 14 degrees. Now take Hardknott at 1 in 3: 100 divided by 3 is 33%, and the angle is about 18.4 degrees. So a slope that sounds steep as a percentage is a surprisingly small angle, and this is why a hill of 18 degrees feels so much steeper than it looks on paper.
Frequently asked questions
What does 1 in 3 mean?
The road rises 1 unit for every 3 units horizontally, which is about 33%.
Is 100% gradient vertical?
No. A 100% gradient is a 45 degree slope.
Why does the same road have two gradients?
Different surveys measure different stretches, along different lines, and signs are rounded.
How do I convert percent to 1-in-x?
Divide 100 by the percent. 25% is 1 in 4.