Degree to Pitch Calculator: Slope & Angle Converter

This calculator converts an angle in degrees to a pitch ratio (rise over run) and a percentage slope, plus the inverse. Enter an angle in degrees or a pitch ratio (e.g., 6/12), and you get the corresponding roof pitch, gradient, or incline value you need for construction, engineering, or design.

Formula

The core math is simple trigonometry. The pitch (rise over run) is the tangent of the angle:

pitch = tan(angle)

where angle is in degrees. Conversely, the angle is the arctangent of the pitch:

angle = arctan(pitch)

Slope percentage is just the pitch multiplied by 100: slope% = pitch × 100. For example, a pitch of 0.5 means the surface rises 0.5 units for every 1 unit of horizontal run — a 50% slope.

Worked Example

Using the default values: angle = 30°, pitch = 0.577.

1. Convert 30° to radians: 30 × π/180 = 0.5236 radians.
2. Take the tangent: tan(0.5236) = 0.5774.
3. So the pitch is 0.577 (rise/run), and the slope percentage is 57.7%.
4. Check the reverse: arctan(0.577) = 30°.

The calculator shows pitch = 0.577 and slope = 57.7%, matching the manual calculation.

How to Read the Results

The pitch ratio is usually written as “X in 12� for roofs (e.g., 6/12 means 6 inches of rise per 12 inches of run). To get that, multiply the pitch by 12. For example, a pitch of 0.577 × 12 = 6.93, so a 30° roof is roughly a 7/12 pitch. Slope percentage is common for roads, ramps, and land grading: a 100% slope is a 45° angle (because tan(45°) = 1).

Remember that the tangent function is not linear: doubling the angle does not double the pitch. A 10° slope is 17.6%, but a 20° slope is 36.4% — not double. Always use the calculator or a tangent table for accurate conversions.

Common Mistakes and Pitfalls

• Mixing degrees and radians: Most construction calculators expect degrees, but many programming languages use radians. Always check the mode.
• Confusing pitch with slope percentage: Pitch is a ratio (rise/run), while slope percentage is that ratio times 100. A 1:1 pitch is a 100% slope, not 1%.
• Using rise over run vs. rise over hypotenuse: Some people mistakenly use the sine function, which gives the ratio of rise to the sloped length, not the run. For roofs and ramps, you need the tangent.
• Rounding too early: If you round the pitch to 0.58 and then compute the angle, you get 30.1° instead of 30°. Keep extra digits during intermediate steps.

When to Use This Calculator

Use it whenever you need to switch between an angle and a slope ratio. Common scenarios:

• Roof framing: converting a blueprint angle to a rafter pitch.
• Wheelchair ramp design: checking that the slope meets accessibility guidelines (usually 1:12 or less).
• Road and driveway grading: expressing grade as a percentage.
• Stair stringer layout: determining the angle from the rise and run.
• Landscaping: setting drainage slopes (typically 1-2% for flat areas).

For very small angles (less than 5°), the pitch in percent is approximately equal to the angle in degrees times 1.75, but the tangent formula is exact and always safe.

Limits of the Formula

The tangent function is undefined at 90° (infinite pitch), and the calculator will show an error or a very large number for angles close to 90°. In practice, pitches above 12/12 (45°) are rare for roofs, but they do occur in some architectural styles. For angles above 45°, the pitch grows quickly: 60° is a 173% slope, and 80° is a 567% slope. The arctangent conversion works for any positive pitch, but remember that a vertical wall has infinite pitch, which cannot be expressed as a finite number.

Also note that the calculator assumes a two-dimensional slope. If you are working with a 3D slope (e.g., a diagonal on a roof plane), you need to account for the true horizontal run, which may require more complex geometry.

Frequently Asked Questions

How do I convert a roof pitch like 6/12 to degrees?

Divide the rise by the run (6/12 = 0.5), then take the arctangent: arctan(0.5) ≈ 26.57°. So a 6/12 roof is about 26.6°.

What is a 45-degree angle in pitch?

A 45° angle has a tangent of 1, so the pitch is 1:1, or 12/12 in roof terms, and the slope percentage is 100%.

Is a 100% slope the same as a 90-degree angle?

No. A 100% slope means the rise equals the run, which is a 45° angle. A 90° angle is vertical and has infinite slope.

Why does my pitch calculator show a different result than my phone’s app?

Check whether the app is using degrees or radians. Also, some apps display pitch as a ratio like “1:4� instead of a decimal. The math is the same, but the formatting differs.

Can I use this for a wheelchair ramp?

Yes, but always verify against local building codes. A common standard is a 1:12 slope (about 4.76°), but requirements vary. This calculator gives you the angle for any ratio, but it does not provide legal advice.

What is the difference between pitch and slope?

In construction, pitch is often the ratio of rise to span (total width), while slope is rise over run. This calculator uses rise over run, which is the standard for roofs and ramps. Always confirm which definition your project uses.

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in a | Angle (degrees) | deg | 30 | 0
in p | Pitch (rise/run) | - | 0.577 | 0
out pitch | Pitch (rise:run) | - | tan(a * pi / 180) | 3
out percent | Slope (%) | % | tan(a * pi / 180) * 100 | 1
out angle | Angle (degrees) | deg | atan(p) * 180 / pi | 1