Calculate Slope Between Two Elevations

To calculate slope between two elevations, divide the vertical change by the horizontal distance between the points. Enter both elevations and the horizontal distance to get the slope as a ratio, percentage, and angle; use consistent units for the elevation and distance.

Formula

The basic slope formula is:

Slope (%) = (ending elevation − starting elevation) ÷ horizontal distance × 100

• Starting elevation (e1): the first point’s elevation, in metres in this calculator.
• Ending elevation (e2): the second point’s elevation, in the same unit.
• Horizontal distance (d): the level, plan-view distance between the points, in metres here.
• Rise: e2 − e1, the signed vertical change.

The ratio output expresses the vertical change for each unit of horizontal distance: rise per 1 horizontal. The angle is arctangent of rise divided by horizontal distance, converted to degrees. If the ending point is lower, rise, percentage, and angle are negative; the ratio formula shown is intended for an uphill positive rise.

Worked Example

Using the calculator’s defaults, the starting elevation is 100 m, ending elevation is 120 m, and horizontal distance is 200 m.

1. Find the rise: 120 m − 100 m = 20 m.
2. Divide rise by horizontal distance: 20 ÷ 200 = 0.1.
3. Convert to a percentage: 0.1 × 100 = 10.00%.
4. Express the ratio: 200 ÷ 20 = 10.00, or 1 unit up for every 10 units across (1:10).
5. Find the angle: arctan(20 ÷ 200) = 5.71°.

What the Result Means

A 10% uphill slope rises 10 units vertically for every 100 units of horizontal distance. It does not mean the surface is at a 10-degree angle. In this example, the angle is about 5.71 degrees. Percent grade and angle are different ways to describe the same rise-to-run relationship.

For a downhill route, keep the points in their travel order. If elevation falls from 120 m to 100 m over 200 m, the signed grade is −10%, indicating descent. If you only need steepness regardless of direction, use the absolute value: 10%.

Horizontal Distance, Ground Distance, and Units

The denominator in the standard grade formula is horizontal distance—the distance measured on a level map or plan—not the length along the sloping ground. If you use the slope-surface length instead, the result will be slightly different. For a slope angle θ and surface length L, horizontal distance is L × cos(θ); when the angle is unknown, survey or map data can provide the horizontal distance directly.

Elevation change and distance must use matching units before division. Convert feet to feet or metres to metres; for example, a rise of 50 ft over 1,000 ft gives 5%, not 0.05%. Mixed units need conversion: 10 m of rise over 100 ft is about 32.81 ft of rise over 100 ft, or 32.81%.

The calculation works in either metric or US customary units because it is a ratio. A 10 m rise over 100 m and a 10 ft rise over 100 ft both equal 10%. Elevation values can be relative to any shared datum; only their difference affects the result.

When to Use Slope and How to Measure It

This calculation is useful for describing a trail, road, ramp, roof, land parcel, or a segment of a surveyed route. Pick two defined points, obtain their elevations from a reliable measurement or map, and measure the horizontal separation between them. For a long or irregular route, calculate separate segments rather than treating the whole route as one uniform incline.

• Use points that correspond to the same route or alignment; otherwise the distance and elevation change may describe different paths.
• For a local grade, place points close enough to capture the section of interest. A long baseline averages dips and steep sections together.
• Record whether the result is signed or absolute. The sign communicates uphill versus downhill when point order is known.
• Keep appropriate precision in the input data, but avoid reporting more decimal places than the measurements justify.

Common Mistakes and Limits

A frequent error is confusing a 10% grade with a 10° angle. A 10% grade corresponds to about 5.71°, while a 10° angle corresponds to a grade of about 17.63% because 100 × tan(10°) ≈ 17.63.

Another mistake is using the total elevation at the ending point as the rise. The rise is the difference between elevations, not the ending elevation itself. Also check that the distance is horizontal and that units match. Rounding the elevations or distance too early can noticeably affect a short or gently sloping segment.

This formula reports an average grade between two points. It cannot show every change in steepness between them, and it does not account for terrain roughness, curves, surface conditions, or measurement uncertainty. A detailed profile requires multiple elevation-distance observations. For engineering, construction, or accessibility decisions, use suitable survey data and applicable project requirements rather than relying on a single average.

Frequently Asked Questions

What is the formula for slope between two elevations?
Subtract the starting elevation from the ending elevation, then divide by horizontal distance. Multiply by 100 for percentage grade: (e2 − e1) ÷ d × 100.

How do I calculate slope as a percentage?
Divide the vertical rise by horizontal run and multiply by 100. A 3 m rise over 60 m is 5%.

Is a 10% slope the same as a 10-degree slope?
No. A 10% grade is about 5.71°. A 10° angle is about a 17.63% grade.

Can slope be negative?
Yes. When the ending elevation is lower than the starting elevation, the signed slope is negative, which indicates a downhill direction for the chosen point order.

Should I use horizontal distance or distance along the slope?
Use horizontal distance for the standard rise-over-run grade formula. Surface distance is longer than horizontal distance on an incline and should not be substituted without conversion.

Can I calculate slope from elevations alone?
No. You also need the horizontal distance between the points. Elevation difference by itself gives rise, not slope.

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in e1 | Starting elevation | m | 100 | 0
in e2 | Ending elevation | m | 120 | 0
in d | Horizontal distance | m | 200 | 0
out pct | Slope | % | (e2 - e1) / d * 100 | 2
out ratio | Rise per 1 horizontal | 1:n | d / (e2 - e1) | 2
out angle | Slope angle | degrees | atand((e2 - e1) / d) | 2