Rise Over Run Calculator

The rise over run calculator converts the two simplest measurements of an incline — vertical rise and horizontal run — into every derived value you need for construction, road design, roofing, landscaping or mathematics: slope, angle of inclination, percentage grade, 1:n ratio, hypotenuse (actual surface length) and X-in-12 roof pitch. It also works in reverse: enter the slope and one dimension to solve for the unknown rise or run.

What “rise over run” means

Every inclined surface or straight line can be described by two measurements taken at right angles to each other:

• Rise — how far up (or down) you travel in the vertical direction.
• Run — how far you travel horizontally.

Their ratio — rise ÷ run — is the slope. A rise of 3 metres over a run of 12 metres gives slope = 3 ÷ 12 = 0.25. The same incline expressed differently is:

All five representations describe the exact same incline; this tool shows them all at once.

How it works

The core formula is simple:

slope (m) = rise ÷ run

From there, three further results follow directly:

1. Angle — θ = arctan(rise / run). The inverse tangent of the slope gives the angle the surface makes with the horizontal plane, in degrees.
2. Percentage grade — grade = m × 100. Used by road and rail engineers to express steepness as a percentage (a 6 % grade means 6 m of rise per 100 m of run).
3. Hypotenuse — h = √(rise² + run²). Pythagoras’ theorem gives the actual length along the slope — the quantity you need when ordering timber, ramp material or sheet roofing.

The calculator also computes the 1:n ratio as 1 : (1/slope) and the X-in-12 pitch as (rise/run) × 12, both common in construction and carpentry.

Reverse solving

Sometimes you know the target slope and one dimension and need the other:

• Solve for Rise — enter slope and run; the tool computes rise = slope × run.
• Solve for Run — enter slope and rise; the tool computes run = rise ÷ slope.

This is particularly useful when designing ramps: you know the height difference (rise) and the allowed gradient (slope), so you solve for the required horizontal footprint (run).

Worked example — wheelchair ramp

A building entrance is 0.15 m above pavement level. Accessibility guidance recommends a maximum gradient of 1 in 12 (slope = 0.0833).

1. Set Solve for: Run.
2. Enter Rise = 0.15 m, Slope = 0.0833.
3. The calculator returns Run = 1.80 m.
4. The hypotenuse — the actual ramp surface length — is √(0.15² + 1.80²) = 1.806 m.

So the ramp needs a horizontal footprint of 1.80 m and approximately 1.81 m of physical ramp material. Add handrails at the sides and you’re meeting the 1:12 standard.

Worked example — roof pitch

A rafter spans a half-width of 6 ft (run) and the ridge is 2 ft above the wall plate (rise).

1. Set Solve for: Slope, Units: feet.
2. Enter Rise = 2, Run = 6.
3. Slope = 0.333 · Angle = 18.43° · Pitch = 4-in-12 · Hypotenuse = 6.32 ft (rafter length).

A 4-in-12 pitch is common on US and UK residential roofs — shallow enough for easy walking, steep enough for adequate drainage.

Formula note

All four outputs derive from the same right-angled triangle whose legs are rise (opposite side) and run (adjacent side):

slope   = rise / run
angle   = atan(rise / run)              [radians → degrees × (180/π)]
grade % = (rise / run) × 100
hyp     = sqrt(rise² + run²)            [Pythagoras]
pitch   = (rise / run) × 12            [X-in-12 notation]

No external libraries are used. Every number is calculated live in your browser using JavaScript’s built-in Math.atan2, Math.sqrt and standard arithmetic — nothing is ever uploaded or stored.