Rise Over Run to Degrees Calculator
Turn any slope into an angle: enter rise and run to get degrees, grade %, ratio and roof pitch — or work backwards from a known angle. Includes a degrees ↔ percent ↔ ratio converter, a live triangle diagram, common-slope and roof-pitch tables, and worked examples.
🔒 100% client-side — your numbers never leave this pageRise + Run → Angle
The classic slope solver: angle = atan(rise ÷ run). Same unit for both (feet, meters, inches — the angle is unit-free).
Angle + Run → Rise
You know the slope angle and the horizontal distance: rise = run × tan(angle).
Angle + Rise → Run
You know the slope angle and the vertical change: run = rise ÷ tan(angle).
Roof Pitch (x/12) → Degrees
Roofers quote pitch as rise over a fixed 12-unit run: angle = atan(x ÷ 12).
Converter: Degrees ↔ Grade % ↔ Ratio
Type in any one field — the other two follow. Grade % = tan(degrees) × 100.
Common slopes: ratio, degrees & grade
Everyday slopes with their angle and grade percent — from wheelchair ramps to roof pitches.
| Ratio (rise:run) | Angle | Grade | 1 in N | Typical use |
|---|---|---|---|---|
| 1:20 | 2.86° | 5% | 1 : 20 | accessible route max (ADA) |
| 1:12 | 4.76° | 8.33% | 1 : 12 | wheelchair ramp (ADA) |
| 1:10 | 5.71° | 10% | 1 : 10 | gentle driveway |
| 1:8 | 7.13° | 12.5% | 1 : 8 | steep driveway |
| 1:6 | 9.46° | 16.67% | 1 : 6 | landscaping swale |
| 1:5 | 11.31° | 20% | 1 : 5 | yard drainage |
| 1:4 | 14.04° | 25% | 1 : 4 | 3/12 roof pitch |
| 1:3 | 18.43° | 33.33% | 1 : 3 | 4/12 roof pitch |
| 7:11 | 32.47° | 63.64% | 1 : 1.57 | typical stair (7″ riser, 11″ tread) |
| 1:2 | 26.57° | 50% | 1 : 2 | 6/12 roof pitch |
| 2:3 | 33.69° | 66.67% | 1 : 1.5 | 8/12 roof pitch |
| 3:4 | 36.87° | 75% | 1 : 1.33 | 9/12 roof pitch |
| 1:1 | 45° | 100% | 1 : 1 | 12/12 roof pitch, 45° |
| 2:1 | 63.43° | 200% | 1 : 0.5 | very steep slope |
| 3:1 | 71.57° | 300% | 1 : 0.33 | ladder-like |
| 10:1 | 84.29° | 1000% | 1 : 0.1 | near-vertical wall |
Roof pitch (x/12) to degrees
Standard US roof pitches converted to angle and grade. A 12/12 pitch is exactly 45°.
| Roof pitch | Angle | Grade |
|---|---|---|
| 1/12 | 4.76° | 8.33% |
| 2/12 | 9.46° | 16.67% |
| 3/12 | 14.04° | 25% |
| 4/12 | 18.43° | 33.33% |
| 5/12 | 22.62° | 41.67% |
| 6/12 | 26.57° | 50% |
| 7/12 | 30.26° | 58.33% |
| 8/12 | 33.69° | 66.67% |
| 9/12 | 36.87° | 75% |
| 10/12 | 39.81° | 83.33% |
| 11/12 | 42.51° | 91.67% |
| 12/12 | 45° | 100% |
Worked examples
Stair stringer: 6 ft rise, 10 ft run
A deck stair rises 6 ft over a 10 ft horizontal run.
atan(6 ÷ 10) = 30.96°, grade 60%, simplified ratio 3:5 — inside the typical 30–37° stair range.
Roof pitch 7/12
A 7/12 pitch means 7 units of rise per 12 of run.
atan(7 ÷ 12) = 30.26°, a 58.33% grade — steeper than the common 6/12 (26.57°) but shallower than 12/12 (45°).
Known angle 30°, run 8 ft → rise
rise = 8 × tan(30°) = 4.62 ft.
At 30°, every foot of run buys 0.577 ft of rise (tan 30° ≈ 0.5774).
Known angle 36.87°, rise 3 → run
run = 3 ÷ tan(36.87°) = 4.
The 3-4-5 triangle — rise 3, run 4, angle 36.87° — is a handy sanity check for any slope calculator.
How the math works
θ = atan(rise ÷ run) × 180 / π → degreesgrade % = (rise ÷ run) × 100 | ratio = rise : runrise = run × tan(θ) | run = rise ÷ tan(θ) | roof pitch x/12 → θ = atan(x ÷ 12)The angle is unit-free: rise and run just need the same unit. Note that degrees and grade percent are not proportional — they are linked by the tangent function, so 45° is a 100% grade, not a 50% grade.
Frequently asked questions
How do I calculate rise over run in degrees?
Use the arctangent: angle = atan(rise ÷ run), then convert radians to degrees by multiplying by 180/π. For example, a rise of 3 with a run of 4 gives atan(3/4) = 36.87°. On a scientific calculator use the atan or tan⁻¹ button, and make sure it is set to degree mode, not radians.
What is the formula for slope angle, grade percent, and ratio?
One rise/run pair gives you all three: angle = atan(rise/run) in degrees, grade = (rise/run) × 100 percent, and ratio = rise:run. A 6 rise over a 10 run is 30.96°, a 60% grade, and a 3:5 ratio.
How do I find the rise if I know the angle and the run?
Rearrange the formula: rise = run × tan(angle). For a 30° slope with a 10 ft run, the rise is 10 × tan(30°) = 5.77 ft. With an 8 ft run at the same angle, the rise is 4.62 ft.
How do I find the run if I know the angle and the rise?
Use run = rise ÷ tan(angle). For example, an angle of 36.87° with a rise of 3 gives a run of 3 ÷ tan(36.87°) = 4. A 45° angle always gives a run exactly equal to the rise.
How do I convert a roof pitch like 6/12 to degrees?
A roof pitch of x/12 is a rise of x over a run of 12, so the angle is atan(x/12). A 6/12 pitch is atan(6/12) = 26.57°, a 7/12 pitch is 30.26° (a 58.33% grade), and a 12/12 pitch is exactly 45°.
What is the difference between grade percent and degrees?
They are related by the tangent function, which is not linear: grade% = tan(degrees) × 100. A 45° slope is a 100% grade, a 30° slope is a 57.74% grade, and a 60° slope is a 173.21% grade. Doubling the degrees does not double the grade percent.
What angle is a wheelchair ramp (ADA)?
The ADA maximum ramp slope is 1:12 — one unit of rise per twelve units of run — which is an 8.33% grade and an angle of 4.76°. Always check your local building code before building; this tool calculates the geometry only and is not code-compliance advice.
Is this the same as a railroad grade calculator?
No. This is a general-purpose rise-over-run slope calculator for stairs, ramps, roofs, and driveways. Our separate railroad grade lab is built specifically for model railroads — helix design, curve compensation, and riser planning — while our percent-to-ratio calculator converts between percent and ratio forms without angles. Each tool covers its own job; this one covers the angle.
Free tool by NRTechStudio