Slope percentage:
rise divided by run, as a percent

Three ways of saying how steep something is

Roads, ramps, drains and hillsides are described in three different ways. A grade or slope percentage says how many units of height are gained per 100 units of horizontal distance. A ratio such as 1:20 says one unit of rise for every 20 of run. An angle gives the incline in degrees from horizontal. They are all the same information in different wrappers, and conversions between them come up constantly in construction, drainage and accessibility work.

Percentage is the most common on road signs and in site drawings because it is easy to scale: a 5 % grade gains 5 m of height over 100 m, or 50 cm over 10 m.

The formula

Run is measured level, not along the surface. If you pace along the incline you have the hypotenuse, and using it in the formula makes the slope look a bit lower than it is. For gentle slopes the difference is small, but for steep ones it is significant.

Worked example: 0.6 m rise over 12 m

As a ratio, 0.05 is 1 in 20. As an angle, the inverse tangent of 0.05 is about 2.86 degrees. A ramp this gentle is easy for a wheelchair user and walkers will barely notice it.

Percent is not degrees

People expect a 100 % slope to be vertical, but 100 % means rise equals run, which is a 45 degree incline. A truly vertical face has an infinite grade because the run is zero. So percentages above 100 are possible and simply mean steeper than 45 degrees: a 200 % slope rises 2 for every 1 of run, about 63.4 degrees.

To go from percent to degrees use angle = arctan(slope % ÷ 100), and to go back use slope % = tan(angle) × 100. For small angles below about 10 degrees, the percentage is approximately 1.75 times the angle in degrees; the rule breaks down on steeper slopes.

Ramp and drainage checks

Many accessibility standards limit ramps to around 1:12, which is 8.33 %, and prefer gentler. A rise of 0.3 m on a 1:12 ramp needs a run of 0.3 × 12 = 3.6 m, which is easy to verify with the formula: 0.3 ÷ 3.6 × 100 = 8.33 %. Check the code that applies in your area, since limits, landings and handrail rules vary.

Drains work the opposite way: a minimum fall is needed, not a maximum. Surface drains and paved areas are commonly laid with a gentle fall of around 1 to 2 %, but check the specification, because pipe diameters and local rules differ.

• A 2 % fall over 10 m is 0.2 m, or 20 cm.
• To get a 1.5 % fall over 8 m you need a drop of 0.015 × 8 = 0.12 m.
• Steeper than about 12 to 15 % starts to feel demanding to walk or cycle up.

Slope in roads, rail and drainage

Road signs warn of grades such as 6 % or 8 %, which means a rise of 6 or 8 metres for every 100 metres travelled horizontally. A 6 % climb over 2 km gains about 120 m of height. Railways use much gentler gradients, often expressed as 1 in 100, which is 1 %, because steel wheels on steel rails have limited grip.

Surface drainage is the opposite concern: water has to move. A paved yard might be laid to fall at 1 in 60, which is 1.67 %, so a 12 m wide yard drops 0.2 m across. Sewer pipes need a minimum gradient to keep solids moving, and the figure depends on pipe size and local regulations, so check the relevant standard instead of relying on a rule of thumb.

For cyclists, 3 % feels gentle, 6 % is a real climb for most riders and 10 % is steep. A road at 10 % over 1 km gains 100 m.

Handling slope and distance together

Sometimes you know the sloping length and the grade rather than the run. For a slope of 5 % and a sloping distance of 100 m, the run is 100 × cos(2.86°) ≈ 99.9 m and the rise is 100 × sin(2.86°) ≈ 5.0 m. For gentle slopes the difference between slope length and run is negligible, so most civil engineers treat them as the same up to about 10 %.

For steeper slopes the difference grows. A 50 % slope has an angle of 26.57 degrees. Over a sloping distance of 100 m, the run is 89.4 m and the rise is 44.7 m, which is 50 % of the run. If you used the sloping distance as the run, you would compute 44.7 ÷ 100 = 44.7 %, a quite noticeable error.

Getting the numbers on site

1. 1Fix a string line level between two points, using a line level or a spirit level on a straight edge.
2. 2Measure the horizontal distance between the points; that is your run.
3. 3Measure the vertical drop from the string to the ground at the far end; that is the rise.
4. 4Divide rise by run and multiply by 100.