Slope and Gradient Calculator
Convert between percentage grade, ratio, angle and elevation difference for a slope.
Formula
Gradient is rise over run. The angle is the arctangent of the same fraction.
- Grade (%) = Rise ÷ Run × 100
- Angle (°) = arctan( Rise ÷ Run )
- Ratio = Run ÷ Rise, written as 1 : ratio
- Slope length = √( Run² + Rise² )
Worked example
A road rising 2.5 m over 100 m horizontally.
- Grade = 2.5 ÷ 100 × 100 = 2.5%
- Angle = arctan(0.025) = 1.43°
- Ratio = 100 ÷ 2.5 = 40, so 1:40
- Slope length = √(100² + 2.5²) = 100.03 m
2.5% grade, 1:40, about 1.43° from horizontal.
Assumptions and limitations
- Run is the horizontal distance, not the distance measured along the sloping surface. Confusing the two produces a small but real error on steep slopes.
- The calculator treats rise as a magnitude. Whether it is a rise or a fall depends on your direction of travel.
- Ratio is expressed as vertical:horizontal, so 1:40 means one unit up for forty along.
What this calculator does not do
- Does not check the slope against any standard. Minimum drainage falls, maximum road gradients and accessibility limits come from the governing specification.
- Does not assess slope stability. Whether an earth batter will stand at a given angle is a geotechnical question.
- Does not set out levels or chainages. It converts between ways of expressing one slope.
Practical tips
- Percentage and ratio are the same information in different clothes: 2% is 1:50, 1% is 1:100. Being fluent in both saves arguments on site.
- Drainage falls are usually specified as a ratio and are small — often between 1:40 and 1:100 for pipework. Small errors matter because the fall is small.
- On slopes shallower than about 10%, the slope length is barely longer than the horizontal distance. Above 20% the difference becomes significant for material quantities.
Frequently asked questions
How do I convert a percentage grade to a ratio?
Divide 100 by the percentage. A 2% grade is 100 ÷ 2 = 1:50. A 5% grade is 1:20.
What does 1:40 fall mean?
One unit of vertical drop for every forty units of horizontal distance — a 2.5% grade. Over a 4 m run that is 100 mm of fall.
Is gradient the same as angle?
They describe the same slope but are not numerically equal. A 100% grade is 45 degrees, not 90. The relationship is angle = arctan(grade ÷ 100).
Should I measure the horizontal distance or the slope distance?
Gradient is defined on the horizontal distance. If you have measured along the ground on a steep slope, that figure is longer than the true run and will understate the gradient.
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Estimating tool, not a design. This calculator works out quantities from the dimensions you enter. It does not size any structural member, verify a design, or confirm compliance with any building code. Check every result against your project specification and applicable local standards, and involve a qualified engineer where the work requires one.