What to measure
Slope from two points
The slope m = (y₂ − y₁) ÷ (x₂ − x₁) — “rise over run”. Once you have m, the line through the points is y = mx + b, where b = y₁ − m·x₁.
Worked example: (2, 3) and (6, 11)
- m = (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2
- b = 3 − 2 × 2 = −1, so y = 2x − 1
- Angle = arctan(2) = 63.43°; distance = √(4² + 8²) = 8.9443
When both differences are whole numbers, the result is also shown as a reduced fraction, such as (0, 0) and (4, 3) → 3/4.
Slope from rise and run
For ramps, driveways, roofs and yard grading, you usually know the height change (rise) over a horizontal distance (run).
- Grade % = rise ÷ run × 100
- Angle = arctan(rise ÷ run)
- Pitch = rise per 12 units of run (roofs are quoted as “4 in 12”, “6 in 12”)
Worked example: a ramp rising 1 ft over 12 ft
- 1 ÷ 12 = 0.0833 → 8.33% grade, 4.76°, ratio 1 : 12
- 1 inch of rise per foot; the ramp surface is 12.04 ft long
Common slopes
| Use | Typical slope |
|---|---|
| ADA wheelchair ramp (max) | 1:12 · 8.33% |
| Ground away from a foundation (min) | 6 in in 10 ft · 5% |
| Patio drainage | ⅛–¼ in per ft · 1–2% |
| Low-slope roof | under 3 in 12 |
Rise per foot to grade and angle
Rise per 12 in of horizontal run.
| Rise per foot | Grade | Angle | Ratio |
|---|---|---|---|
| 1/8 in | 1.04% | 0.6° | 1 : 96 |
| 1/4 in | 2.08% | 1.19° | 1 : 48 |
| 1/2 in | 4.17% | 2.39° | 1 : 24 |
| 1 in | 8.33% | 4.76° | 1 : 12 |
| 2 in | 16.67% | 9.46° | 1 : 6 |
| 4 in | 33.33% | 18.43° | 1 : 3 |
| 6 in | 50% | 26.57° | 1 : 2 |
| 12 in | 100% | 45° | 1 : 1 |
Common mistakes
- Measuring the run along the slope. Run is the horizontal distance; a tape laid on the ground or the ramp surface measures the longer sloped length.
- Mixing units by hand. Rise in inches over run in feet gives a number 12 times too big; convert both to the same unit first (the calculator does it for you).
- Reading grade as degrees. An 8.33% grade is 4.76°, not 8.33°.
- Subtracting in a different order. Take y₂ − y₁ and x₂ − x₁ from the same point first, or the sign of the slope flips.
Frequently asked questions
How do you 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 (2, 3) and (6, 11) that's 8 ÷ 4 = 2.
What is a 1:12 slope?
One unit of rise for every 12 units of run — an 8.33% grade, or about 4.76°. It's the steepest slope the ADA allows for a wheelchair ramp.
How do I convert slope to a percentage?
Divide rise by run and multiply by 100. A 1 ft rise over 20 ft is 5%. The angle is the arctangent of rise ÷ run.
What is the slope of a vertical line?
Undefined, because the run (x₂ − x₁) is zero and you can't divide by zero. A horizontal line has a slope of 0.
How much should a yard slope away from a house?
Building codes commonly call for the ground to fall at least 6 inches within the first 10 feet from the foundation — a 5% grade — so water drains away.
How many degrees is a 1/4 inch per foot slope?
About 1.19°. It's a 2.08% grade, or a ratio of 1:48.
What angle is a 6 in 12 roof pitch?
26.57°. Six inches of rise per foot of run is a 50% grade, or 1:2.
Is a 100% slope vertical?
No. A 100% grade means the rise equals the run, which is 45°. A vertical line has an undefined slope.
Sources
Formulas and defaults last reviewed October 30, 2026. How we check our math.