Slope & Gradient Calculator
Enter vertical rise and horizontal run to calculate gradient percentage, degrees and a 1:n slope ratio for roads, trails and site planning.
By Aryan Khan, Founder & Editor · Updated October 2026
For example, a rise of 3 feet over a 40-foot run is a 7.5% grade, a 4.29° angle and a 1 : 13.3 ratio — one slope, three correct ways to say it.
How to use Slope Percent to Degrees Calculator
Two measurements in, every dialect of steepness out:
The Slope & Gradient Calculator converts a rise and a run into the three standard ways of stating steepness: percent grade, slope angle in degrees, and rise-over-run ratio. Enter the two measurements in any matching unit and read all three — no translating between road crews, architects and trig tables.
- 1Enter vertical rise.
- 2Enter horizontal run in the same unit.
- 3Read percent grade, angle and slope ratio.
What people use Slope & Gradient Calculator for
1. Roof pitch translation
Roofers speak in pitch (rise per 12 of run): a 6-in-12 roof is a 50% grade and a 26.57° angle. This is the translator between the roof and the building code.
2. Cycling climb analysis
Race profiles quote percent; your legs feel angle. Convert a climb's numbers before the ride, and check its true length with the Slope Length Calculator.
3. Pipe and sewer falls
Drainage specs come as ratios (1 : 80, 1 : 40). Read them as percent and angle here so the fall you dig is the fall the drawing meant.
4. Landscaping and grading plans
Swales, banks and accessible paths each carry a target steepness in a different dialect. One conversion up front prevents three phone calls later.
Worked examples
Rise equals run and the slope is 100% grade at exactly 45°. Everything steeper is more rise than run — a fact that makes 'a 200% grade' sound dramatic and a 63.4° slope sound merely technical.
A path rising 1 m over 20 m of run: 5% grade, 2.86°, ratio 1 : 20. Gentle to walk, and right at the edge of what many accessibility guidelines treat as a ramp rather than a path — the number decides which rules apply.
Steepness in three dialects
Computed (angle = atan(rise ÷ run)) — pin the row your project speaks.
| Percent grade | Angle | Ratio | Feels like |
|---|---|---|---|
| 1% | 0.57° | 1 : 100 | Drainage fall |
| 5% | 2.86° | 1 : 20 | Gentle path |
| 8.33% | 4.76° | 1 : 12 | Steepest common ramp standard |
| 12% | 6.84° | 1 : 8.3 | Hard cycling climb |
| 50% | 26.57° | 1 : 2 | 6-in-12 roof pitch |
| 100% | 45.00° | 1 : 1 | The diagonal itself |
Percent and degrees part company as slopes grow: doubling the grade does not double the angle. At small grades they nearly agree, which is exactly why the confusion survives.
Understand grade as percent, angle and ratio
Road signs, trail profiles and engineering drawings describe slope in different ways. Percent grade is rise divided by horizontal run multiplied by 100, while the angle in degrees comes from the arctangent of the same ratio. A 1:n ratio expresses the same geometry in another familiar form.
Keep rise and run in the same unit before calculating. The result describes the average slope between two points; real terrain or roads can contain steeper short sections that an average does not reveal.
How to interpret the result
The most common errors come from using a correct result to answer the wrong geographic question. Keep these points in mind for Slope & Gradient Calculator:
- Treat climate and hardiness outputs as 30-year character, not this year's weather: a zone tells you what winters usually allow, and microclimates — walls, slopes, urban heat — shift a real garden half a zone either way.
- Remember that elevation models see bare terrain: no buildings, no forest canopy. A line-of-sight 'clear' verdict can still be blocked by a wood, and a horizon distance assumes open ground — treat results as the terrain baseline, then add land cover from local knowledge.
Limits & appropriate use
Terrain intelligence carries one dominant limit: the model sees bare earth at ~90 m spacing with metres of vertical error, and is blind to canopies, walls and wires. Every downstream answer inherits it — profiles show terrain truth with noisy amplitude, line-of-sight verdicts are pending trees, horizons assume open ground, and solar radiation averages assume an unshaded panel. The second limit is temporal: climate letters and hardiness zones are thirty-year character, not this year's behaviour, and seismicity is a mood, not a hazard model. Each result here is printed with its recipe precisely so these boundaries travel with the number.
The value proposition is screening-grade truth at zero cost: orientation for sites, gardens, antennas, shoots and curiosity, with the upgrade points clearly marked. When money or safety attaches to the answer — tower siting, flood insurance, structural shading, avalanche terrain — the escalation is professional: licensed survey, certified shade studies, regulatory flood determinations and geological hazard services. A good free tool makes that ladder visible instead of pretending to be the top of it.
- Construction and tower siting → licensed topographic survey.
- Flood decisions → regulatory determinations (FEMA/FIRM in the US).
- Solar finance → certified shade and production studies.
Data & methodology
Grade = rise/run × 100; slope angle = atan2(rise, run).
For source details, licences and model limitations, see Data Sources and Methodology.
Key terms worth knowing
- Antipode
- The diametrically opposite point; latitude flips, longitude shifts 180°.
- Köppen class
- The letter-code climate system from temperature/precipitation thresholds.
Editorial guidance: MapBench explains the method and limitations so the tool can be used as a transparent reference, not as a black-box answer. For legal boundaries, safety-critical routing, surveying, engineering, regulated decisions or official statistics, verify the result with the responsible authority or a qualified professional.
Category: Earth Science. Results are intended for everyday analysis and planning unless a page explicitly states otherwise.
Method, assumptions & limits
- This tool’s method
- Grade = rise/run × 100; slope angle = atan2(rise, run).
- Before relying on the answer
- Check the location, height units and any model options shown by this calculator. A terrain lookup and a geometric Earth model answer different questions.
- What the result cannot establish
- Local terrain, atmospheric conditions and source resolution can matter more than numerical rounding. Do not use a planning result for safety-critical work.
Coverage: Worldwide. Search, basemap and external data requests may use third-party services; browser-based does not mean every operation is offline. Read the source and licence notes, calculation methodology and privacy policy. If a result looks inconsistent, report a correction with the inputs and mode used.
Frequently asked questions
Clear answers about the calculation, accuracy and appropriate use.
What is a 10% grade?
A 10% grade means 10 units of vertical change for every 100 units of horizontal distance.
Is percent grade the same as degrees?
No. Grade is 100 × rise/run; angle is arctangent(rise/run).
Is this suitable for engineering or legal decisions?
Treat the result as planning or educational context unless the page explicitly says otherwise. Engineering, hazard and legal decisions should use authoritative specialist data.
Why can terrain data differ between sources?
Elevation and earth datasets vary in resolution, collection date and processing method. Small local features may not be represented equally.
Can I verify the data source?
Yes. MapBench documents major providers and methodology on the Data Sources and Methodology pages.
How do I convert percent grade to degrees?
Take the arctangent of the grade as a decimal: angle = atan(percent ÷ 100). Ten percent is atan(0.10) = 5.71°. The calculator does it both ways.
What does a 1 : 12 ratio mean in percent?
One unit of rise per twelve of run: 1 ÷ 12 = 8.33%. Ratios divide the other way from how they are often read aloud — 'one in twelve' is rise over run.
Which unit should my rise and run be in?
Any unit, as long as both match — feet with feet, metres with metres. Grade, angle and ratio are unit-free because the units cancel in the division.
Can the run be measured along the slope?
That distance is the slope length, not the run. Using it as the run understates steepness slightly; on a 10% grade the error is about half a percent of the value.
Why do roof pitches use 12?
The foot-based trade convention: pitch states inches of rise per 12 inches (one foot) of run. A 4-in-12 pitch is a 33.3% grade at 18.43°.
Is a negative slope meaningful?
It records direction — a fall rather than a rise. Drainage and road profiles use the sign; the steepness magnitude is identical.
What is the steepest this can express?
As the run approaches zero the grade runs to infinity and the angle to 90°. Vertical faces are the limit the mathematics points at but roads never reach.
Related tools and resources
Grades from a path: the Slope Grade Calculator; slope distance: the Slope Length Calculator; relief: the Relief Ratio Calculator.
More free tools
Sources, methodology & editorial trust
- ✓ Browser-first processing where supported
- ✓ External sources are documented
- ✓ No account required for public tools
- ✓ Review data sources
Calculations are documented with their assumptions, limitations and source context rather than presented as unexplained answers.
Reviewed and maintained by Aryan Khan, Founder & Editor of MapBench.
Part of our elevation & terrain hub
Slope & Gradient Calculator sits in the elevation & terrain cluster, alongside 40 other tools that answer neighbouring questions with different methods or datasets.
You may also need
When this answer is only part of the job, these clusters cover the next step.
Read the guide behind this tool
How to Find Elevation on Google Maps — Check the elevation of any spot on Google Maps — desktop, mobile, and the precise method with exact numbers.