Elevation Degree Calculator: Find an Angle from Rise and Run

An elevation degree calculator finds the angle of a slope from its vertical rise and horizontal run. Enter both measurements in the same unit to get the angle in degrees, plus the slope as a percentage and the distance along the slope.

Formula

The angle above horizontal is the inverse tangent of rise divided by horizontal run:

θ = arctan(r ÷ d)

• θ is the elevation angle in degrees.
• r is the vertical rise in metres.
• d is the horizontal run in metres.

The calculator also gives grade, calculated as 100 × r ÷ d, and slope distance, calculated with the Pythagorean theorem: √(r² + d²). The input unit is metres, but the ratio used for the angle and grade is unchanged if both measurements are entered in feet, inches, or another consistent unit. The displayed slope distance uses the same unit as the inputs.

Worked Example

With the default rise of 3 m and horizontal run of 4 m:

1. Angle: arctan(3 ÷ 4) = arctan(0.75) ≈ 36.87°.
2. Grade: 100 × 3 ÷ 4 = 75.00%.
3. Slope distance: √(3² + 4²) = √25 = 5.00 m.

The calculator reports the angle to two decimal places. Its underlying result is approximate because displayed values are rounded.

What an Elevation Degree Calculator Measures

“Elevation angle” describes the angle between a level, horizontal line and a line that rises or falls. It is also called an angle of elevation when the direction is upward. The calculator uses two sides of a right triangle: the vertical change and the horizontal separation. Their ratio determines the angle, so the actual size of the triangle does not matter. A rise of 3 m over 4 m has the same angle as a rise of 3 ft over 4 ft.

This is different from elevation as an altitude, which is a height above a reference such as sea level. An altitude by itself does not tell you the slope angle. You also need the horizontal distance between the points, or a direct angle measurement.

How to Measure Rise and Run

Rise is the difference in height between the two endpoints. Run is the horizontal distance between them—not the length measured along the sloping surface. This distinction matters: using the slope length as the run will generally produce an incorrect angle.

• Measure the vertical change between the lower and higher points.
• Measure the horizontal distance between those same points.
• Convert both measurements to the same unit before comparing them.
• Enter nonnegative values. If both are zero, there is no defined direction or angle.

For a long or uneven route, the result represents the overall angle between its endpoints. It does not describe every local change in steepness along the way. A route that goes up and down can have a modest net rise even if some sections are steep.

Reading Degrees, Percent Grade, and Slope Distance

Degrees describe the angle directly: 0° is level, and an angle approaching 90° is nearly vertical. Percent grade describes rise divided by horizontal run, multiplied by 100. For example, 75% grade means 75 units of rise for every 100 units of horizontal run; it does not mean an angle of 75 degrees.

The two measures are related but not interchangeable. Grade is 100 × tan(θ), while the angle is arctan(grade ÷ 100). A 45° angle corresponds to a 100% grade, not a 45% grade. The slope distance is the straight-line distance along the incline. In a 3-4-5 triangle, the rise and run are 3 and 4, while the sloping side is 5.

Common Mistakes and Calculator Limits

• Mixing units: A rise in metres and a run in feet cannot be divided meaningfully until one is converted. The angle ratio is unitless, but its two lengths must use matching units.
• Confusing run with slope length: Run is horizontal. If you know the slope distance instead, calculate the horizontal component from the available geometry before using this calculator.
• Reading percent as degrees: A grade of 10% is about 5.71°, not 10°.
• Ignoring direction: This calculator uses nonnegative rise and run, so it returns an upward angle from 0° to less than 90°. For a downhill direction, record the angle as negative separately or specify the direction in your notes.

The calculation assumes a straight line between the endpoints and a level horizontal reference. It does not account for curved terrain, measurement error, or changes in slope along a path. When rise is zero and run is positive, the result is 0°. When run is zero and rise is positive, the ideal geometry is vertical, or 90°; the formula’s ratio form is undefined at exactly zero run, so that case should be treated as a vertical line rather than entered as an ordinary slope calculation.

Frequently Asked Questions

How do you calculate an elevation angle?
Divide vertical rise by horizontal run, then take the inverse tangent: θ = arctan(rise ÷ run). Use a calculator set to degrees, or use the calculator above.

Is a 10% slope the same as 10 degrees?
No. A 10% grade means rise is one tenth of horizontal run. Its angle is arctan(0.10), approximately 5.71°.

Can I enter feet instead of metres?
Yes, if both rise and run are in feet. The angle and percentage grade are unchanged. The displayed slope distance will then be in feet despite the unit label in the example setup, so use the same units consistently when interpreting that output.

What does a 45-degree elevation mean?
It means the slope rises one unit for each horizontal unit, because tan(45°) = 1. Its grade is 100%.

How do I find the angle if I know the slope length?
You need enough information to determine the vertical rise or horizontal run as well. Slope length alone does not uniquely identify the angle: many different right triangles can have the same sloping side.

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in r | Vertical rise | m | 3 | 0
in d | Horizontal run | m | 4 | 0
out angle | Elevation angle | degrees | atand(r / d) | 2
out grade | Grade | % | 100 * r / d | 2
out slope | Slope distance | m | sqrt(r^2 + d^2) | 2