Elevation Grade Calculator

Grade (%) = rise ÷ (run × 12) × 100, with the rise in inches and the run in feet

R

Vertical rise, the height gained or lost

L

Horizontal run, measured level, not along the slope

G

Grade, the rise written as a percentage of the run

θ

Slope angle from the horizontal, in degrees

Use it wherever water has to run or a surface has to be walkable: a driveway graded away from the garage, a yard that must drain to a swale, a patio that must not pond, a ramp, a raised bed that needs its top soil level. The whole answer comes from two numbers, so measure them properly — a level and a rule, not an eye.

1. A 12 ft run rising 12 inches

   1. Rise: 12 inches
   2. Run in inches: 12 × 12 = 144 inches
   3. Grade: 12 ÷ 144 = 0.0833, so 8.33%
   4. Ratio: 1 ÷ 0.0833 = 12, written as 1:12
   5. Angle: the arctangent of 0.0833, which is 4.76°
   6. In metric: 8.33 cm of fall per metre of run

   1:12 is the ratio you will see written on a ramp or a roof detail, and it is the same slope as 8.33% or 4.76° — three ways of saying one thing, which is why all of them are on the result panel.

2. A 24 ft driveway falling 3 ft to the road

   1. Rise: 3 ft = 36 inches
   2. Run in inches: 24 × 12 = 288 inches
   3. Grade: 36 ÷ 288 = 0.125, so 12.5%
   4. Ratio: 1:8
   5. Angle: arctan(0.125) = 7.13°
   6. Per foot of run: 1.5 inches of fall

   A car will not notice the 12.5% itself — it will notice the crease where the driveway meets the road. That transition is what scrapes a bumper, and easing it over a few feet costs less than regrading the whole run.

This is the grade of one straight slope: the run is horizontal distance and the rise is vertical, which is what a level and a rule give you. A slope that curves or eases partway has to be split into sections and each one entered on its own — an average over the whole run hides the steepest part, and the steepest part is the one that matters for a car, a wheelchair or a drain. The grade says nothing about cross-fall, about the surface, or about how fast water actually moves: 2% on concrete and 2% on loose gravel shed water very differently. Anything that has to satisfy a code — a ramp, a roof, a storm connection — is judged against that code's own tolerances and exceptions, not against this arithmetic.

How do I work out a grade percentage?

Divide the rise by the run in the same unit, then multiply by 100. Twelve inches of rise over a 12 ft run is 12 ÷ 144 = 0.0833, so an 8.33% grade. A 1% grade is one unit of fall per 100 units of run, which is why the percentage is the easiest of the four to sanity-check by eye.

What is a 1:12 slope in percentage and degrees?

8.33% and 4.76°. The ratio and the percentage are the same number written two ways: 1 ÷ 12 = 0.0833. Ramp and roof details are usually drawn as a ratio, drainage and road plans as a percentage, and a survey as degrees — three notations for one slope.

How much fall does a drainage slope need?

A drainage slope of 1% to 2% is the usual range for a surface channel, a swale or a yard: over 10 metres that is 10 to 20 centimetres of fall. Below about 0.5% water stops moving on a rough surface, and well above 2% it runs fast enough to scour bare ground.

Should the run be measured level or along the slope?

Level. Grade is rise over horizontal distance, and the gap between the two grows with the steepness: on a 12.5% slope the distance along the surface is 0.8% longer than the level run, and on a 1:12 ramp it is 0.3% longer. A tape laid on the ground measures the slope, so a long run needs a level and a plumb line.

How do I convert a percent grade into degrees?

Take the arctangent of the rise divided by the run. A 100% grade is 45°, because rise and run are equal; 50% is 26.57°, 20% is 11.31° and 8.33% is 4.76°. The two scales only look alike near zero: a 20% grade is 11.31°, not 20°, because the rise and the run stop being a small triangle.

What grade can a driveway have?

Most driveways are built somewhere between 4% and 15%: enough slope to shed water away from the house, shallow enough that a car does not scrape at the transition to the street. The bottom of the driveway is the part to check — a short, steep flare there is what grounds a bumper, and no overall percentage warns you about it.

• Approximate Conversions from U.S. Customary Measures to Metric — the chart behind the inch, foot, centimetre and metre conversions used here — National Institute of Standards and Technology
• The International System of Units (SI) brochure — the definition of the metre, on which every length conversion on this page rests — Bureau International des Poids et Mesures (BIPM)