Slope is calculated by dividing the vertical rise by the horizontal run. To express slope as a percentage, multiply the result by 100. To find the slope angle in degrees, use the inverse tangent (arctan) of rise divided by run.
Slope percentage = (Rise / Run) × 100
Slope angle = arctan(Rise / Run)
For example, a surface that rises 2 metres over a horizontal run of 10 metres has a slope of 0.2, or 20%. Its angle is approximately 11.31°.
Slope calculations are used in roofing, ramps, drainage, roads, stairs, landscaping, and other construction projects. Rise and run help determine roof pitch, driveway grade, drainage gradients, and the angle of an inclined surface.
When calculating slope between two points on a graph, use the coordinate formula. Subtract the first point's y-coordinate from the second point's y-coordinate, then divide by the difference between their x-coordinates.
m = (y₂ − y₁) / (x₂ − x₁)
Slope is commonly expressed as a decimal, percentage, ratio, angle, or roof pitch. Although these formats describe related measurements, each uses a different representation and requires the correct conversion.
Use the slope calculator to calculate slope from rise and run or work with percentage and angle values.
What Is Slope?
Slope describes how much a surface rises or falls over a horizontal distance. In construction, the two measurements used to calculate slope are usually called rise and run.
Slope Terminology
Slope is the relationship between vertical rise and horizontal run. The same relationship is written in different ways depending on the trade or the subject.
| Term | Meaning |
|---|---|
| Rise | Vertical change in height between two points. |
| Run | Horizontal distance over which the rise occurs. |
| Slope / gradient | Rise divided by run — how steep a line or surface is. |
| Slope percentage | Slope expressed as a percentage: (rise ÷ run) × 100. |
| Slope ratio | Rise to run written as a ratio, such as 1:5. |
| Slope angle | Angle of the incline measured from horizontal, in degrees. |
| Point-slope form | y − y₁ = m(x − x₁). |
| Slope-intercept form | y = mx + b, where m is slope and b is the y-intercept. |
Rise and run must use the same unit. A 200 mm rise and a 5 metre run cannot be divided until the millimetres are converted — the construction unit converter handles that step quickly.
The Slope Formula
The slope formula is the version used in coordinate geometry to find the slope of a line given two points:
The numerator is the vertical change and the denominator is the horizontal change. In plain terms, slope is rise over run.
How to Find Slope with Two Points
- Label the points (x₁, y₁) and (x₂, y₂).
- Subtract the y-values: y₂ − y₁ is the rise.
- Subtract the x-values: x₂ − x₁ is the run.
- Divide the rise by the run.
Example: slope of a line through (2, 3) and (6, 11)
Rise = 11 − 3 = 8. Run = 6 − 2 = 4.
Slope = 8 ÷ 4 = 2. The line rises 2 units for every 1 unit it moves right.
How to Find Slope Between Two Points on a Graph
When a graph is supplied instead of coordinates, mark any two clear points on the line, count the vertical units and the horizontal units between them, then divide. Counting upward gives a positive rise; counting downward gives a negative rise.
A line that climbs from left to right has a positive slope, a line that descends has a negative slope, a horizontal line has zero slope, and a vertical line has an undefined slope because the run is zero.
Point-Slope Form and Slope-Intercept Form
Once the slope is known, the equation of the line can be written two ways. With the slope m and one point (x₁, y₁):
Rearranged into slope-intercept form, the same line reads:
Here m is the slope and b is the value where the line crosses the y-axis.
How to Calculate Slope Percentage
The slope percentage formula divides the rise by the run and multiplies by 100:
Example: 2 m rise over 10 m run
Slope percentage = (2 ÷ 10) × 100 = 20%
The surface rises 20 vertical units for every 100 horizontal units. The percentage is measured against the horizontal run, never against the sloping length.
How to Calculate Slope Angle
The slope angle uses the same rise and run, passed through the inverse tangent:
Most scientific calculators provide this as tan⁻¹ or atan. Confirm the calculator is set to degrees when the answer is needed in degrees.
Example: 2 m rise and 10 m run
Rise ÷ Run = 0.20
Angle = arctan(0.20) ≈ 11.31 degrees
How to Calculate Slope Ratio
A rise of 2 units over a run of 10 units is written as 2:10 and simplifies to 1:5. Conventions vary between industries, so confirm whether a drawing expects a ratio, a percentage or an angle before quoting a figure.
Finding Rise or Run When One Is Unknown
Rearranging the slope percentage formula gives either missing measurement.
An 8% slope over a 12 metre run requires a rise of (8 ÷ 100) × 12 = 0.96 m.
A 0.75 metre rise at a 5% slope needs a run of 0.75 ÷ 0.05 = 15 m.
Slope Percentage to Angle Conversion Table
Percentage and angle do not increase at the same rate. A 100% slope is 45 degrees, not 100 degrees.
| Slope Percentage | Decimal Slope | Angle (degrees) |
|---|---|---|
| 1% | 0.01 | 0.57° |
| 2% | 0.02 | 1.15° |
| 5% | 0.05 | 2.86° |
| 10% | 0.10 | 5.71° |
| 15% | 0.15 | 8.53° |
| 20% | 0.20 | 11.31° |
| 25% | 0.25 | 14.04° |
| 30% | 0.30 | 16.70° |
| 40% | 0.40 | 21.80° |
| 50% | 0.50 | 26.57° |
| 75% | 0.75 | 36.87° |
| 100% | 1.00 | 45.00° |
Worked Construction Examples
Example 1: Access ramp
A ramp rises 0.6 metres over a horizontal run of 8 metres.
Slope percentage = (0.6 ÷ 8) × 100 = 7.5%
Angle = arctan(0.6 ÷ 8) ≈ 4.29 degrees
Allowable grades depend on the project, accessibility requirements and local regulations, so treat the figure as a starting point rather than a compliance check.
Example 2: Drainage run
A drain falls 150 mm over 12 metres. Convert first: 150 mm = 0.15 m.
Slope percentage = (0.15 ÷ 12) × 100 = 1.25%
Because the surface falls, the same grade is written as −1.25% when direction matters, as it does on drainage and road drawings.
Example 3: Roof rise and run
A roof rises 2.5 metres over a run of 5 metres.
Slope = 2.5 ÷ 5 = 0.5 → Slope percentage = 50%
Angle = arctan(0.5) ≈ 26.57 degrees
Scaled to a 12-unit run, the same roof is a 6:12 pitch.
Roof Pitch vs Slope
Roof pitch is normally written as a rise-to-run ratio, while roof slope may be a decimal, percentage or angle. A 6:12 pitch rises 6 units for every 12 horizontal units:
Pitch also changes the surface length of a roof. A steeper roof has a longer sloping surface than its horizontal footprint, which affects material quantities. The roof pitch calculator converts between pitch, percentage and angle, the roofing calculator handles material estimates, and how to calculate roof area explains the measurement behind it. For the notation differences, see roof pitch vs roof slope and how to calculate roof pitch.
Where Slope Calculations Are Used
- Driveways and ramps. Slope percentage shows how quickly an inclined surface changes elevation. Verify grades against project and accessibility requirements.
- Drainage and grading. Small percentages are specified as a grade or as a fall over a stated horizontal distance. Direction is recorded with a negative sign when the surface falls.
- Roads and paths. Grades are quoted as percentages, positive for a rise and negative for a fall in the measured direction.
- Roofing. Pitch converts directly to slope percentage and angle when comparing roof geometry.
- Stairs. Stair geometry uses rise and run, with additional requirements for riser height, tread depth, landings and headroom — see how to calculate stair dimensions.
For general measurement conventions across trades, the construction measurements guide covers units and common tolerances.
Common Slope Mistakes
- Using sloping length instead of run. The run is horizontal. Substituting the hypotenuse changes the result.
- Mixing units. Convert millimetres to metres before dividing.
- Reading percentages as degrees. A 20% slope is about 11.31°, not 20°.
- Assuming pitch and slope notation are identical. Confirm whether a drawing asks for a ratio, decimal, percentage or angle.
- Dropping the sign. Falling grades need a negative value for drainage, road profiles and site grading.
- Rounding too early. Keep extra decimal places through the calculation and round only the final answer.
Frequently Asked Questions
How do you calculate slope percentage?
Divide the rise by the run and multiply by 100. A 2 m rise over a 10 m run gives (2 ÷ 10) × 100 = 20%.
How do you calculate slope angle?
Use arctan(rise ÷ run). For a 2 m rise over a 10 m run, arctan(0.20) ≈ 11.31°.
What is the slope of a 10% grade?
A decimal slope of 0.10, equal to approximately 5.71 degrees.
What is a 50% slope in degrees?
A decimal slope of 0.50, equal to approximately 26.57 degrees.
Is slope percentage the same as slope angle?
No. Percentage compares rise to run on a 100 scale, while angle is measured in degrees from horizontal. A 100% slope equals 45 degrees.
How do you find the slope of a line through two points?
Use m = (y₂ − y₁) ÷ (x₂ − x₁). Subtract the y-values for the rise, subtract the x-values for the run, then divide.
Can slope be calculated in feet or inches?
Yes, provided rise and run use the same unit. Slope percentage and angle are unit-independent.
Can a slope be negative?
Yes. A negative slope shows a falling grade — the surface drops as you move in the measured direction.
Slope Calculation Summary
- Slope of a line: m = (y₂ − y₁) ÷ (x₂ − x₁)
- Slope percentage: (rise ÷ run) × 100
- Slope angle: arctan(rise ÷ run)
- Slope ratio: rise : run, simplified
- Roof pitch: rise : 12
Every format begins with the same two measurements. Keep the units consistent, use the horizontal run rather than the sloping length, and round at the end. The slope calculator is useful for repeated conversions, but the formulas above let you verify any result on site or in an exam.