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Grade From Elevation Calculator

Enter start and end elevations and horizontal distance to find the slope grade.

Result

8.00%
36.00
4.57°

How it is calculated

The tool takes the start elevation, the end elevation and the horizontal distance (the run). The rise is rise = elev₂ − elev₁. The grade is grade % = rise ÷ run × 100, and the angle is angle = arctan(rise ÷ run) converted to degrees. All three lengths must be in the same unit; the rise is shown in that same unit, and the grade and angle are the same if you use feet for everything. The run must be greater than zero. Going downhill gives a negative rise, grade and angle, with the same size as the uphill case. Run means horizontal distance, not the distance along the slope, which is longer.

Worked example

A path starts at 312 m and ends at 348 m, over a horizontal distance of 450 m. Rise = 348 − 312 = 36.00 m. Grade = 36 ÷ 450 × 100 = 8.00%. Angle = arctan(36 ÷ 450) = arctan(0.08) = 4.57°. Walking the same path in the other direction gives −8.00% and −4.57°, the same steepness going down. For comparison, a grade of 100% would be a 45° slope.

Try this example →

Common mistakes

  • Using the distance measured along the slope as the run. A tape laid along the path is longer than the horizontal distance, which makes the grade look lower than it really is.
  • Mixing units, such as elevations in metres and distance in kilometres. Convert all three values to one unit first, or the grade is off by a factor of 1,000.
  • Confusing percent grade with degrees. An 8% grade is only 4.57°, and 45° is a 100% grade, not 45%.
  • Swapping the start and end elevations. This only flips the sign, but a negative result then reads as a descent when you meant a climb.
  • Leaving the run at zero. A vertical drop has no defined percent grade, so the tool returns no result.

About this calculator

Slope grade expresses steepness as a percentage: the vertical rise divided by the horizontal run, multiplied by 100 — Grade % = ((End elevation − Start elevation) / Horizontal distance) × 100 — which is different from the slope angle in degrees, though the two are related by angle = arctan(rise/run). A 100% grade is a 45° slope, not vertical, which is a common point of confusion.

Grade percentage is the standard unit used in road and trail construction, civil engineering drawings, and outdoor recreation: highway grades are typically kept under about 6–8%, ADA-compliant wheelchair ramps must generally stay at or below 8.3% (1:12), and hiking or cycling routes are often rated by their steepest sustained grade.

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Comments (1)

  • Editorial team

    A percent grade is easy to turn into the ratio you may prefer: divide 100 by the grade. The preset 5.00% is a rise of 1 for every 20 of horizontal distance, and 8% is about 1 in 12.5. Roads, trails, railways and roof pitches are often described in different forms, so convert before comparing figures from different sources. What are you measuring with it, a road, a trail, a ramp or a roof?

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