Slope Conversion Calculator: % Grade to Degrees

This slope conversion calculator converts between four common ways of expressing slope: percent grade, degrees, rise over run (as a ratio), and rise per 100 units of run. You enter any one of these values, and the calculator returns the other three, so you can switch between construction, engineering, and road-sign conventions instantly.

Formula

Percent grade is the rise divided by the run, multiplied by 100. In symbols:

Percent grade = (rise / run) × 100

Degrees measure the angle of the slope above horizontal. The tangent of that angle equals rise over run:

tan(θ) = rise / run

So to convert from percent grade to degrees:

θ = arctan(percent grade / 100)

And to convert from degrees to percent grade:

Percent grade = 100 × tan(θ)

Where:

• rise = vertical change (same unit as run, e.g., meters, feet)
• run = horizontal distance (same unit as rise)
• percent grade = rise/run × 100 (unitless, but expressed as %)
• θ = angle of slope in degrees (or radians for calculations)

Worked Example

Using the default value of 10% grade:

1. Start with percent grade = 10%.
2. Convert to a decimal: 10 / 100 = 0.10.
3. Find the angle: θ = arctan(0.10). Using a calculator, arctan(0.10) ≈ 5.7106°.
4. So a 10% grade is equivalent to about 5.71 degrees.
5. The rise:run ratio is 1:10 (since rise/run = 0.10, which is 1/10).
6. The rise per 100 units of run is 10 (because 10% means 10 units up for every 100 units horizontally).

The calculator shows the same results: percent grade 10.00%, degrees 5.71°, ratio 1:10, and rise per 100 = 10.00.

Why Slope Conversion Matters

Different fields use different slope notations, and converting between them is a daily need for many professionals:

• Road construction uses percent grade on signs (e.g., “6% gradeâ€� on a highway).
• Roofing uses rise over run (e.g., “4/12â€� roof pitch).
• Civil engineering often uses degrees for steep slopes and percent for gentle ones.
• Cycling and hiking apps commonly display percent grade.
• Accessibility ramps are usually specified in percent or ratio (e.g., 1:12).

If you’re working with a drawing that says “slope 1:20� and you need to know the angle for a tool, or you see a road sign “10%� and want to know the angle, this calculator bridges the gap.

How to Use the Calculator

Enter a value in any one of the three input fields: percent grade, degrees, or rise:run ratio. Leave the other two blank (or at zero). The calculator will compute the remaining values. For example:

• Enter 15 in the percent grade field → get degrees ≈ 8.53°, ratio 1:6.67, rise per 100 = 15.
• Enter 30 in the degrees field → get percent grade ≈ 57.74%, ratio 1:1.73, rise per 100 ≈ 57.74.
• Enter 0.5 in the ratio field (meaning 0.5 rise per 1 run, i.e., 1:2) → get percent grade = 50%, degrees ≈ 26.57°.

The ratio input expects the rise per one unit of run, not a colon notation. So for a 1:12 roof pitch, enter 1/12 ≈ 0.0833.

Common Mistakes and Misconceptions

One frequent error is mixing up percent grade with degrees. A 45° slope is not 45% – it’s 100%! Because tan(45°) = 1, and 1 × 100 = 100%. So a 100% grade is a 45° angle. Many people think 100% grade would be vertical, but vertical is undefined (infinite percent).

Another mistake is using the wrong tangent function on a calculator – make sure it’s in degree mode when you input degrees. If you’re doing the math manually, remember to convert degrees to radians for most programming languages.

Also, don’t confuse “rise over run� with “rise over hypotenuse� (the slope length). Slope is always vertical change divided by horizontal change.

Limitations and Accuracy

This calculator assumes a straight, uniform slope. Real-world slopes (hills, ramps, roads) are rarely perfectly straight, but the conversion applies to the average slope between two points. For very steep slopes (over 45°), the tangent function grows rapidly, and small measurement errors in the rise or run lead to large changes in the angle. For slopes over 90° (overhanging), the formulas break down – but such slopes are not typical in construction.

Also, the calculator uses the arctangent function, which returns values between -90° and +90°. For slopes expressed as positive numbers, you’ll get a positive angle. For negative grades (downhill), the calculator will return a negative angle, which is correct for direction.

Finally, always verify the units: rise and run must be in the same unit. If you have a rise of 1 meter and a run of 10 feet, convert one to the other first (e.g., 10 ft = 3.048 m, so grade = 1/3.048 × 100 ≈ 32.8%).

Alternatives to This Calculator

If you need to convert between slope and other measurements, you might also use:

• Inclinometer / clinometer – a physical tool that measures degrees directly.
• Smartphone apps – many use the phone’s accelerometer to measure slope in degrees.
• Construction calculators – dedicated devices that handle pitch, grade, and angle conversions.
• Spreadsheet formulas – in Excel, use =DEGREES(ATAN(grade/100)) and =TAN(RADIANS(deg))*100.

But for a quick, free, and accurate conversion, this online calculator is the simplest option.

Frequently Asked Questions

What is a 1% slope in degrees?

A 1% slope means rise/run = 0.01. The angle is arctan(0.01) ≈ 0.57°. So a 1% grade is just over half a degree.

How steep is a 10% grade?

A 10% grade means you rise 10 units for every 100 units horizontally. That’s about 5.7 degrees. For comparison, a typical residential street is 5-10% grade, and a steep mountain road might be 15-20%.

What does a 100% slope mean?

A 100% slope means rise equals run, so the angle is 45°. It’s not vertical – vertical would be infinite percent. A 100% grade is quite steep, like a very steep staircase or a black diamond ski run.

How do I convert roof pitch (e.g., 6/12) to degrees?

Roof pitch is rise over run in inches per 12 inches. So 6/12 means rise = 6, run = 12. First compute the ratio: 6/12 = 0.5. Then degrees = arctan(0.5) ≈ 26.57°. You can enter 0.5 in the ratio field of this calculator to get the same result.

Is a 5% grade the same as a 5° slope?

No. A 5% grade is about 2.86°. A 5° slope is about 8.75% grade. They are very different. Always check which unit you’re dealing with.

Can I use this for ADA ramp requirements?

You can use the calculator to convert the required slope (e.g., 1:12) to degrees or percent, but you must check the specific accessibility code in your area for exact limits. The calculator just does the math; it doesn’t provide legal or safety advice.

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in p | Percent grade | % | 10 | 0
in d | Degrees | ° | 0 | 0
in rr | Rise per run (e.g. 1:12) | - | 0 | 0
out grade | Percent grade | % | (p + d * 100 * tan(d * pi / 180) + (rr > 0 ? rr : 0)) | 2
out deg | Degrees | ° | atan((p / 100) + (d * pi / 180) + (rr > 0 ? atan(rr) : 0)) * 180 / pi | 2
out ratio | Rise:Run ratio | - | (p > 0 ? 1 : (d > 0 ? 1 / tan(d * pi / 180) : (rr > 0 ? 1 / rr : 0))) | 2
out per100 | Rise per 100 | - | (p + d * 100 * tan(d * pi / 180) + (rr > 0 ? rr * 100 : 0)) | 2