Maths & geometry Australia
Slope Calculator
Enter a rise and a run β or two points β and every way of expressing that slope appears at once: percentage grade, angle in degrees, and the 1-in-X ratio that drainage and access work is specified in.
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Any unit, as long as both match
Measured level, not along the slope
Percentage grade
βRatio
β
Angle
β
Slope (m)
β
Slope length
β
How do you calculate slope?
Divide the rise by the run. That fraction is the slope: multiply it by 100 for a percentage grade, take its arctangent for the angle in degrees, or invert it for a 1-in-X ratio. A 150 mm fall over 3 metres is 0.05 β a 5% grade, 2.86 degrees, and a 1-in-20 slope.
Four ways to say the same thing
Which form a slope is quoted in usually tells you which trade wrote the specification.
| Form | This example | Used by |
|---|---|---|
| Ratio (1 in X) | 1 in 20 | Drainage, accessible ramps, driveways |
| Percentage grade | 5% | Roads, earthworks, surveying |
| Angle in degrees | 2.86Β° | Engineering, roof pitch, machinery |
| Rise over run | 150 : 3000 | Site measurements and setting out |
The ratio form is the one that causes arguments, because a bigger number means a gentler slope. 1 in 40 is flatter than 1 in 20, which reads backwards against every other measure on this page.
Measuring a run in the field
The run is a horizontal distance, and on sloping ground a tape laid on the surface does not give you one. Over a short distance the error is small enough to ignore. Over a long one it is not: a 30 metre tape pulled down a 20% bank measures about 30.6 metres of surface for 30 metres of run, reporting the grade as roughly 2% flatter than it really is.
The usual field fix is a levelled string line and a rule, or a laser level and a staff, so the horizontal distance is measured horizontally rather than inferred from a sloping tape.
How this is calculated
All four ways of writing a slope come from the same fraction. Rise divided by run is the slope; everything else is that number in different clothes.
slope m = rise Γ· runpercentage grade = m Γ 100angle in degrees = arctan(m) Γ 180 Γ· Οratio = 1 : (run Γ· rise)slope length = β(riseΒ² + runΒ²)
Percentage and degrees are not interchangeable and diverge quickly. A 100% grade is 45 degrees, not 90 β worth remembering whenever a specification quotes one and a tool reports the other.
The run is always the horizontal distance, measured level. Measuring along the face of a slope gives the slope length instead, which is longer, and using it as the run understates the grade. On gentle slopes the difference is negligible; past about 15% it is not.
A worked example: fall on a drainage line
A stormwater line has to fall 150 millimetres across a 3 metre run. What grade is that, and does it clear a 1-in-40 minimum?
- Rise (fall)150 mm
- Run, converted to the same unit3,000 mm
- Slope β 150 Γ· 3,0000.05
- Percentage grade β Γ 1005%
- Ratio β 1 Γ· 0.051 in 20
- Angle β arctan(0.05)2.86Β°
A 5% grade, or 1 in 20 β twice the fall a 1-in-40 minimum would require.
Steeper is not automatically better on a drainage line. Water running too fast can outrun the solids it is meant to carry, which is why plumbing codes specify a range rather than just a floor.
What this calculator does not do
- Assumes a constant slope between the two measurement points β real ground rarely is
- Percentage and degrees only agree at zero; neither is a shortcut for the other
- A ratio in a compliance requirement is a limit, not a target to sit exactly on
- Checks no code requirement β see the ramp and stair calculators for those
Common questions
What does a 1 in 20 slope mean?
One unit of fall for every twenty units of horizontal distance. Over three metres that is 150 millimetres of fall, which is a 5% grade or 2.86 degrees.
Is a 100% grade the same as vertical?
No β it is 45 degrees. A 100% grade means the rise equals the run. Vertical has no run at all, so the percentage is undefined rather than 100.
How do I convert a percentage grade to degrees?
Divide the percentage by 100 to get the slope, then take its arctangent. A 12% grade is arctan(0.12), or 6.84 degrees. The two only track each other closely below about 10%.
Which way round are rise and run?
Rise is vertical, run is horizontal. Slope is rise divided by run, so a large rise over a short run is steep. Reversing them gives the reciprocal, which is the second number in the ratio form.
Can I use this for roof pitch?
Yes. Enter the vertical rise of the roof and the horizontal run from the wall to the ridge, then read the angle in degrees. Roof pitch in Australia is usually quoted in degrees rather than as a ratio.
Where these numbers come from
- Wolfram MathWorld β slope, gradient and arctangent Fixed formula, nothing to go out of date
Method last reviewed 2026-10-28 This calculator uses fixed rules rather than rates that change, and its method is re-checked against the sources above at least once a year. Out of date? Tell us and we will fix it.
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