Calculate Elevation from Slope and Distance

To calculate elevation change from slope and distance, multiply the horizontal distance by the slope expressed as a decimal. Enter the distance and slope percentage below to get the elevation change; the calculator also shows the equivalent rise per unit of distance.

Formula

Elevation change = horizontal distance × slope percentage ÷ 100.

In symbols: Δh = d × (s / 100), where:

• Δh is the vertical elevation change, in metres when the distance is entered in metres.
• d is the horizontal distance, in metres.
• s is the slope, expressed as a percentage.

A slope percentage is the vertical rise divided by the horizontal run, multiplied by 100. For example, a 5% slope rises 5 units vertically for every 100 horizontal units. The second calculator output, rise per 100 m, is therefore numerically equal to the slope percentage when the distance unit is metres.

Worked Example

Using the calculator’s defaults, the horizontal distance is 100 m and the slope is 5%.

1. Convert the percentage to a decimal: 5 ÷ 100 = 0.05.
2. Multiply by the horizontal distance: 100 m × 0.05 = 5 m.
3. Round the elevation change to two decimal places: 5.00 m.

The rise per 100 m is 5.00 m. This result is the change in elevation over the chosen distance, not the absolute elevation of the endpoint. To find an endpoint elevation, add the change for an uphill route or subtract it for a downhill route from a known starting elevation.

What Slope and Distance Mean

Slope describes how quickly elevation changes across a horizontal distance. A 1% slope means a rise or fall of 1 unit for every 100 horizontal units; a 10% slope means 10 units for every 100. The units cancel in the ratio, so the same percentage applies whether measurements are in metres and centimetres, or feet and inches, provided the vertical and horizontal units are consistent.

For example, a road that gains 30 m over 600 m of horizontal distance has a slope of (30 ÷ 600) × 100 = 5%. Conversely, over 600 m at 5%, the elevation change is 600 × 0.05 = 30 m. For US customary measurements, a 5% grade over 1,000 horizontal feet gains 50 ft. If you want the answer in feet but have distance in metres, convert the calculated elevation change: 1 m is approximately 3.28084 ft.

In ordinary use, positive slope indicates a rise and negative slope indicates a descent. This calculator accepts a nonnegative slope percentage, so use it for the size of the change; determine whether to add or subtract that change from the starting elevation based on travel direction.

Horizontal Distance Versus Distance Along a Slope

The standard grade formula uses horizontal distance, sometimes called run. It does not use the length measured along the sloping ground. The distinction is small on gentle slopes but matters more as the slope gets steeper.

If you know the sloping distance instead, and the slope is given as a percentage, the slope angle θ satisfies tan(θ) = s/100. The vertical change can then be found using the sloping distance L: Δh = L × sin(θ), or equivalently Δh = L × (s/100) / √(1 + (s/100)²). For a gentle 5% slope, using the sloping length as though it were horizontal gives a very close approximation, but the horizontal-distance formula remains the standard definition of grade.

Using the Result and Checking Units

Use the result to estimate the elevation difference between two points when the grade is constant across the specified horizontal distance. If slope varies along a route, one average percentage may provide an overall estimate, but it will not describe each section’s rise or fall. For a changing route, calculate each segment separately and add the signed elevation changes.

• Keep distance units consistent with the unit wanted for the answer. Enter metres to get metres, or feet to get feet.
• Convert a percent to a decimal by dividing by 100. A 5% slope is 0.05 in the formula, not 5.
• Use horizontal map or survey distance when calculating grade. A GPS track’s ground distance may follow the terrain instead.
• Keep enough precision during intermediate calculations, then round the final result to suit the measurement’s accuracy.

For instance, if a route has two horizontal sections of 200 m at +4% and 300 m at −2%, the changes are +8 m and −6 m. The net change is +2 m. The total distance alone and a casually chosen “average slope” can conceal the direction and distribution of those changes.

Limits and Common Misconceptions

A slope percentage is not the same as an angle in degrees. Convert grade to angle with θ = arctan(s/100). Thus, a 100% grade corresponds to a 45° angle, not a 100° angle. A 10% grade is approximately 5.71°, not 10°.

The calculation also does not provide absolute elevation, terrain shape, or elevation at every point between endpoints. It assumes the stated slope is representative and constant across the distance. Real roads, paths, and land surfaces may have changing grades, curves, steps, or measurement error. For accurate surveying or construction work, use appropriate measured data and professional methods rather than treating a simple grade estimate as a survey result.

Frequently Asked Questions

How do I calculate elevation gain from a slope percentage?
Multiply horizontal distance by the slope percentage divided by 100. For 250 m at 8%, the gain is 250 × 0.08 = 20 m.

How do I calculate slope if I know elevation change and distance?
Divide the vertical change by horizontal distance, then multiply by 100. A 12 m rise over 300 m is a 4% slope.

Is a 5% slope the same as a 5-degree slope?
No. A 5% grade is an angle of about 2.86°. A 5° angle corresponds to a grade of about 8.75%, found from tan(5°) × 100.

Can I use distance measured along a hill?
Not directly in the standard percentage-grade formula, which requires horizontal distance. For steep slopes, convert the along-slope length using the slope angle or determine the horizontal run.

Does this calculation give the final elevation?
No. It gives the elevation change. Add that change to the starting elevation for an ascent, or subtract it for a descent.

Related

• Calculate the Hypotenuse of a Triangle
• Brace Angle Calculator: Find the Right Angle
• Binary Log Calculator: Find log₂ of Any Number

in d | Horizontal distance | m | 100 | 0
in s | Slope | % | 5 | 0
out e | Elevation change | m | d * s / 100 | 2
out r | Rise per 100 m | m | s | 2