Omikuji Tools Life & Calc

Slope & Angle Calculator

Converts between angle, grade %, 1:n ratio, radians and roof pitch, and solves the slope triangle. Includes ramp, roof and stair guidance.

✨ Features

  • Angle, grade %, 1:n ratio, radians and roof pitch all convert from whichever one you type
  • Solves the triangle: run and rise give slope length and angle; slope length and angle give rise and run
  • Reference figures for ramps (1:12, 1:15), road signs, roof pitch and stair rise/going
  • Diagram of the triangle with labelled angle and lengths, plus result copy and URL sharing

🪄 Use cases

Designing a ramp

Turn a step height into the run you need and check it against 1:12 or 1:15.

Reading a roof pitch

See what a 4 sun pitch is in degrees and percent before ordering materials.

Ground and road gradients

Get the true slope length and angle from a horizontal distance and a height difference.

Checking a staircase

Convert riser and going into an angle and compare it with the code limits.

🔒 Privacy

Every calculation runs in your browser; the numbers you type are never sent to a server. Only when you shorten a share URL is that URL (including your values) sent to the shortening service.

❓ FAQ

What is the difference between grade % and degrees?

Grade percent is the rise per 100 of horizontal run – the tangent of the angle times 100. So 100% is not vertical, it is 45°. The two are not proportional: 10% is about 5.71°, 50% about 26.57°, and 100% exactly 45°, so each extra percent adds less angle than the last. Road signs and treadmills use percent; drawings and surveying usually use degrees.

How do I read a 1:n ratio?

It means one unit of rise for every n units of run. At 1:12, a 10 cm step needs 120 cm of run. Accessibility rules commonly cap ramps at 1:12 (about 4.76°), with 1:15 (about 3.81°) preferred outdoors. The bigger the n, the gentler the slope.

What is a Japanese roof pitch in "sun"?

It is the rise in sun (about 30.3 mm each) for every 10 sun – one shaku, about 303 mm – of run. A 4 sun pitch is 10:4, which is about 21.8° or a 40% grade. Up to 3 sun (about 16.7°) counts as low pitch and needs careful waterproofing, around 5 sun (about 26.6°) is typical, and past 6 sun (about 31°) the roof is too steep to walk on safely.

How is slope length calculated?

By Pythagoras: slope length = √(run² + rise²). If you know the angle instead, slope length = run ÷ cos(angle) = rise ÷ sin(angle). When you are checking whether a ramp fits into a floor plan, remember to use the run rather than the slope length – the run is what the ramp occupies on the drawing.

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Conversions

Type into any one field and the rest are calculated for you.

°
%
1 :
rad
sun
Conversions
-

Grade % is the rise for every 100 of run, 1:n is the run for every 1 of rise, and roof pitch (sun) is the rise for every 10 of run. All representations exist only while the angle is above 0° and below 90°.

Slope triangle

Angle
-
Grade
-
Ratio
-
Slope length
-
Rise
-
Run
-

Lengths can be in any unit (metres, feet, inches) – results come back in the same unit.

Diagram

Diagram - - - -

Reference figures

Ramps (accessibility)

SlopeAngleGrade %
1:87.13°12.5%
1:105.71°10%
1:124.76°8.33%
1:153.81°6.67%
1:202.86°5%

The ADA and most building codes cap ramps at 1:12 (8.33%); 1:15 or gentler is much easier to self-propel in a manual wheelchair. Japan's barrier-free standard is 1/12 indoors and 1/15 outdoors.

Road grade (% signs)

Grade %AngleSlope
3%1.72°1:33.3
5%2.86°1:20
8%4.57°1:12.5
10%5.71°1:10
12%6.84°1:8.3
15%8.53°1:6.7
20%11.31°1:5

The number on a hill sign is the grade in percent. Ordinary roads are designed up to roughly 5–12% depending on design speed; motorways stay nearer 3–5%.

Roof pitch

SunAngleGrade %
1sun5.71°10%
2sun11.31°20%
3sun16.7°30%
4sun21.8°40%
5sun26.57°50%
6sun30.96°60%
8sun38.66°80%
10sun45°100%

A Japanese "4 sun" pitch means 4 units of rise per 10 of run – about 21.8°, or 40%. In imperial terms it is the same idea as 4.8:12. Below 3 sun the detailing has to be watertight; above 6 sun you need scaffolding to work on the roof.

Stairs (rise and going)

cm
cm
Stair angle
-
Grade
-
2 × riser + going
-

Japanese housing stairs are limited to a 23 cm riser and a 15 cm going. A comfortable flight has 2 × riser + going close to 60 cm (about 63–65 cm in most Western rules of thumb).