To calculate slope percentage, divide the rise by the horizontal run and multiply by 100. To calculate the slope angle, use the inverse tangent of rise divided by run.
Slope angle = arctan(Rise / Run)
For example, a slope that rises 2 metres over a horizontal run of 10 metres has a 20% slope. Its angle is about 11.31 degrees.
Slope calculations are used in roofing, ramps, drainage, roads, stairs, landscaping and many other construction measurements. The same basic rise-and-run relationship can describe a roof pitch, a driveway grade or the angle of an inclined surface.
The important part is knowing which form of slope you need. A contractor or plan may express slope as a percentage, ratio, angle or roof pitch. These measurements describe the same basic relationship but are not interchangeable without conversion.
Table of Contents
- What Is Slope?
- How to Calculate Slope Percentage
- How to Calculate Slope Angle
- How to Calculate Slope Ratio
- How to Find Rise or Run
- Worked Slope Examples
- Slope Percentage and Angle Table
- Slope, Roof Pitch and Roofing
- Where Slope Calculations Are Used
- Common Slope Calculation Mistakes
- Use the Slope Calculator
- Frequently Asked Questions
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.
| Term | Meaning |
|---|---|
| Rise | The vertical change in height. |
| Run | The horizontal distance over which the rise occurs. |
| Slope | The relationship between rise and run. |
| Slope percentage | Slope expressed as a percentage. |
| Slope ratio | The relationship between vertical rise and horizontal run. |
| Slope angle | The angle of the inclined surface measured from horizontal. |
The measurements must describe the same direction and use compatible units. You can use metres, feet, inches or another length unit, provided the rise and run are expressed consistently.
How to Calculate Slope Percentage
The slope percentage formula is straightforward. Divide the vertical rise by the horizontal run, then multiply the result by 100.
Example: 2 m rise over 10 m run
Suppose a driveway rises 2 metres over a horizontal distance of 10 metres.
Slope percentage = 20%
The driveway therefore has a 20% slope.
A percentage slope does not mean the surface rises by that percentage of its actual sloping length. It compares the vertical rise with the horizontal run.
How to Calculate Slope Angle
The slope angle is found using the inverse tangent, written as arctan or tan⁻¹. The calculation uses the same rise and run measurements.
Example: 2 m rise and 10 m run
Using the same measurements:
Angle = arctan(0.20)
Angle = approximately 11.31 degrees
So a slope of 2 metres rise over 10 metres horizontal run is approximately 11.31 degrees.
Most scientific calculators have a tan⁻¹, atan or inverse tangent function. Make sure the calculator is set to degrees when you need the answer in degrees.
How to Calculate Slope Ratio
Slope can also be written as a ratio between rise and run. If a surface rises 2 units for every 10 units of horizontal run, the ratio is:
This can be simplified to:
This means the surface rises 1 unit for every 5 units of horizontal run.
Different industries may write slope ratios in different ways, so check the convention being used on the drawing, specification or project instructions. For many construction calculations, the most useful starting point is still the actual rise and run.
How to Find Rise or Run
The slope formula can also be rearranged when one of the measurements is unknown.
Finding rise from slope percentage
For example, if the slope is 8% and the horizontal run is 12 metres:
Rise = 0.96 m
The required vertical rise is 0.96 metres.
Finding run from slope percentage
If the rise is 0.75 metres and the slope is 5%:
Run = 15 m
The horizontal run is 15 metres.
Worked Slope Examples
Example 1: Construction ramp
A ramp rises 0.6 metres over a horizontal run of 8 metres.
Slope percentage = 7.5%
For the angle:
Angle = approximately 4.29 degrees
The ramp therefore has a 7.5% slope and an angle of approximately 4.29 degrees.
Example 2: Drainage slope
A drainage run drops 150 mm over a horizontal distance of 12 metres. First convert the measurements to compatible units:
Then calculate the grade:
Slope percentage = 1.25%
The slope is 1.25%. Because the surface falls rather than rises, it can also be described as a -1.25% grade when direction is important.
Example 3: Roof rise and run
Suppose a roof has a vertical rise of 2.5 metres and a horizontal run of 5 metres.
Slope percentage = 0.5 x 100 = 50%
The slope angle is:
Angle = approximately 26.57 degrees
For a roof, the same rise-and-run measurements can also be expressed as a pitch ratio. In this example, the roof has a 6:12 pitch when the rise is scaled to 6 units for a 12-unit run.
Slope Percentage and Angle Table
The table below shows common slope percentages and their approximate angles. The angle is measured from the horizontal.
| Slope Percentage | Decimal Slope | Approximate Angle | Rise per 100 Run |
|---|---|---|---|
| 1% | 0.01 | 0.57 degrees | 1 |
| 2% | 0.02 | 1.15 degrees | 2 |
| 5% | 0.05 | 2.86 degrees | 5 |
| 10% | 0.10 | 5.71 degrees | 10 |
| 15% | 0.15 | 8.53 degrees | 15 |
| 20% | 0.20 | 11.31 degrees | 20 |
| 25% | 0.25 | 14.04 degrees | 25 |
| 30% | 0.30 | 16.70 degrees | 30 |
| 40% | 0.40 | 21.80 degrees | 40 |
| 50% | 0.50 | 26.57 degrees | 50 |
| 75% | 0.75 | 36.87 degrees | 75 |
| 100% | 1.00 | 45 degrees | 100 |
Slope, Roof Pitch and Roofing
Roof slope and roof pitch are closely related, but the terms are commonly expressed differently. Roof pitch is often written as a rise-to-run ratio such as 6:12, while slope may be expressed as a decimal, percentage or angle.
For example, a 6:12 roof pitch means the roof rises 6 units for every 12 units of horizontal run.
0.50 x 100 = 50% slope
arctan(0.50) = approximately 26.57 degrees
The roof pitch therefore corresponds to a 50% slope and an angle of approximately 26.57 degrees.
Pitch also affects the actual surface distance of a roof. A steeper roof generally has a longer sloping surface than its horizontal footprint. That difference matters when estimating roofing materials.
For more detail, see How to Calculate Roof Pitch and Roof Pitch vs Roof Slope.
Where Slope Calculations Are Used
Slope is not limited to roofs. Rise-and-run calculations appear in many construction and property measurements.
Driveways and ramps
Slope percentage can describe how quickly a driveway, access ramp or other inclined surface changes elevation. Actual allowable grades depend on the project, accessibility requirements, local regulations and site conditions.
Drainage and grading
Small slopes are commonly used when planning drainage and surface grading. A drawing may specify a percentage grade or a rise over a particular horizontal distance.
Roads and paths
Road and pathway grades can be expressed as percentages. A positive percentage normally indicates an increase in elevation in the direction being measured, while a negative percentage indicates a decrease.
Roofing
Roof pitch can be converted into slope percentage and angle when comparing roof geometry or checking measurements.
Stairs
Stair geometry also involves rise and horizontal run, although stair design has additional requirements involving riser height, tread depth, landings and headroom. For stair planning, see How to Calculate Stair Dimensions.
Common Slope Calculation Mistakes
Confusing run with sloping length
The run is the horizontal distance, not the length measured along the slope. Using the sloping length in the basic rise-over-run formula produces a different result.
Mixing units
A rise of 200 mm and a run of 5 metres cannot be divided directly. Convert them first:
Then calculate 0.2 / 5.
Confusing percentage with degrees
A 20% slope is not a 20-degree slope. A 20% slope is approximately 11.31 degrees.
Using roof pitch and general slope terminology as if they are identical
They describe related geometry, but the notation can differ. Always check whether a project specification is asking for a ratio, percentage, decimal slope or angle.
Ignoring direction
A falling grade may need to be represented with a negative sign. This is important for drainage, road profiles and site grading where the direction of the slope matters.
Rounding too early
Keep several decimal places during intermediate calculations and round the final result. Early rounding can introduce avoidable differences in longer measurements.
Use the BuildersMeasures Slope Calculator
If you already know the rise and run, you can calculate slope without doing the trigonometry manually.
Use the BuildersMeasures Slope Calculator to work with rise, run, slope percentage and angle.
The calculator is useful when comparing several measurements or when you need to convert between common slope formats quickly. For important construction work, use the calculated result alongside the project's drawings, specifications and applicable requirements.
Related Construction Calculators and Guides
- Slope Calculator
- Roof Pitch Calculator
- Roofing Calculator
- How to Calculate Roof Area
- How to Calculate Roof Pitch
- Roof Pitch vs Roof Slope
- How to Calculate Stair Dimensions
- Construction Unit Converter
- Construction Measurements Guide
Frequently Asked Questions
How do you calculate slope percentage?
Divide the vertical rise by the horizontal run and multiply by 100. The formula is: slope percentage = (rise / run) x 100.
How do you calculate slope angle?
Divide rise by run and calculate the inverse tangent of the result. The formula is: angle = arctan(rise / run). Set the calculator to degrees when you need the answer in degrees.
What is the slope of a 10% grade?
A 10% grade has a decimal slope of 0.10 and an angle of approximately 5.71 degrees.
What is a 50% slope in degrees?
A 50% slope has a decimal slope of 0.50. Its angle is approximately 26.57 degrees.
Is slope percentage the same as slope angle?
No. Percentage compares rise with horizontal run, while angle describes the inclination of the surface from horizontal. They can be converted using trigonometry.
What is the difference between slope and pitch?
Slope and pitch describe related rise-and-run geometry, but they are commonly written differently. General slope is often expressed as a percentage or decimal, while roof pitch is frequently written as a ratio such as 6:12.
Can I calculate slope from rise and run in feet?
Yes. Feet work just as well as metres or other units as long as the rise and run use the same unit.
Can a slope be negative?
Yes. A negative slope can indicate that elevation decreases in the direction being measured. This is useful when describing drainage, road grades and site profiles.
Slope Calculation Summary
For most construction slope calculations, start with two measurements: rise and horizontal run.
Use (rise / run) x 100 for slope percentage and arctan(rise / run) for slope angle. Keep the units consistent, avoid confusing horizontal run with sloping length, and round only after the main calculation is complete.
BuildersMeasures calculators are intended as practical estimation and planning tools. Verify important project measurements, specifications and applicable requirements before ordering materials or beginning construction work.