How steep is the slope?
Enter rise and run, a percent or two points, get the slope instantly.
Rise and run in the same units — both in inches, feet or centimeters.
How do I calculate slope?
Divide the rise by the run and multiply by 100 for a percent grade. A yard that drops 6 inches over 10 feet (120 inches) has a slope of 6 ÷ 120 × 100 = 5%. The angle is the arctangent of rise ÷ run — 2.86° here — and the ratio is 1 : 20.
How much should the ground slope away from a house?
The International Residential Code asks for a fall of at least 6 inches within the first 10 feet from the foundation — a 5% slope — so rain drains away from the walls. Paved surfaces next to the house need at least 2%.
What is ¼ inch per foot as a percent?
It is 0.25 ÷ 12 = 2.08%. That is the usual minimum slope for drain pipes 2½ inches and smaller, and a common slope for patios; ⅛ inch per foot, 1.04%, is the minimum for larger drain pipes.
How steep can a wheelchair ramp be?
The ADA Standards allow a slope of at most 1 : 12 — one inch of rise for every 12 inches of run, or 8.33%. A 24 inch rise needs at least 24 feet of ramp, plus landings.
How do I convert percent grade to degrees?
Take the arctangent of the grade ÷ 100. A 10% grade is 5.7°, 50% is 26.6° and 100% is 45° — a 100% grade is not vertical, it rises as much as it runs.
How do I find the slope between two points?
Subtract the y values and divide by the difference of the x values: m = (y₂ − y₁) ÷ (x₂ − x₁). For the points (1, 2) and (5, 4): m = (4 − 2) ÷ (5 − 1) = 2/4 = 1/2. The line through them is y = 0.5x + 1.5 — the intercept b = y₁ − m·x₁. A negative slope falls from left to right; if x₁ = x₂ the line is vertical and its slope is undefined.
What is the difference between slope, grade and pitch?
They are the same ratio of rise to run written differently. Grade is a percentage (rise ÷ run × 100), slope is often written as a ratio such as 1:12 or as a decimal, and roof pitch is rise in inches per 12 inches of run. A 6/12 roof pitch is a 50% grade or 26.57°.
Is run measured along the slope or horizontally?
Horizontally. The run is the level distance covered, not the length of the sloping surface. The sloping length is longer: a 3 foot rise over a 40 foot run is 40.11 feet along the surface.
What slope is 1:12 as a percent and in degrees?
One divided by 12 is 8.33%, which is 4.76°. The first number is the rise and the second the run, so 1:12 is a gentle slope and 12:1 would be very steep.
The formulas behind the result
Slope is rise divided by run. Multiplied by 100 it is the percent grade; the angle is the arctangent of rise ÷ run; the ratio form is 1 : (run ÷ rise); and inches per foot is rise ÷ run × 12. The two lengths must be in the same unit, and the run is the horizontal distance. Percent grade and degrees are not proportional: 100% is 45°, a 200% grade is about 63.4°, and a vertical surface would have an infinite grade, so the angle approaches but never reaches 90°. For two points on a graph the same idea gives m = (y₂ − y₁) ÷ (x₂ − x₁), the number the points tab reports together with the intercept.
Worked example: a yard that falls 3 feet in 40 feet
Rise is 3 ft and run is 40 ft, so the slope is 3 ÷ 40 = 0.075, a 7.5% grade. The angle is arctan(0.075) = 4.29°, the ratio is 1 : 13.3, and the fall is 0.9 inches per foot. The surface itself is √(3² + 40²) = 40.11 ft long. That average is above the 5% fall the code asks for in the first 10 feet next to a foundation, but an average can hide a flat spot where water collects, so measure the yard in sections.
Common mistakes
Mixing units is the first one: 6 inches of rise over 10 feet of run is 6 ÷ 120, not 6 ÷ 10, which is 5% rather than 60%. The second is reading a percent as degrees; a 10% grade is 5.7°, not 10°. Third, measuring the run along a tape laid on the slope gives the sloping length, which slightly overstates the run and understates the grade; level the tape or use the horizontal distance. Last, check which direction a requirement is written in: building codes quote a minimum fall for drainage, while accessibility rules quote a maximum slope for ramps.
Sources: 2021 International Residential Code, section R401.3 (drainage away from the foundation); 2010 ADA Standards for Accessible Design, section 405.2 (maximum ramp running slope 1:12); the arctangent and two-point forms are standard trigonometry and analytic geometry (OpenStax Algebra and Trigonometry). Related: roof pitch calculator, stair calculator and right triangle calculator.