What is elevation grade and how is it expressed?

Elevation grade (or slope) describes how steep a surface is. It is most commonly expressed as a percentage — the vertical rise divided by the horizontal run, multiplied by 100. A 5% grade means 5 metres of rise for every 100 metres of horizontal distance. Engineers also use the decimal ratio (0.05), the permille notation (50 ‰) common on railway signs, and the angle in degrees (about 2.86° for 5%).

What is the formula for grade percentage?

Grade (%) = (Rise / Run) x 100. Rise is the vertical change (height gained or lost) and Run is the horizontal distance travelled. If you travel 500 m horizontally and climb 25 m vertically the grade is (25 / 500) x 100 = 5%.

How do I convert grade percentage to degrees?

Angle (degrees) = arctan(Grade% / 100) x (180 / pi). For example a 10% grade gives arctan(0.10) = 5.71 degrees. Note that percentage and degrees are not proportional — a 45-degree slope is 100% grade, and grades above 100% are possible for very steep terrain.

What is slope distance and why is it different from run?

Run is the horizontal (map) distance. Slope distance (also called travel distance or path length) is the actual distance along the sloped surface, which is always longer than the run. By the Pythagorean theorem: Slope distance = sqrt(Rise squared + Run squared). At a 10% grade the slope distance is about 0.5% longer than the run — significant over long distances.

What grade percentage is considered steep for roads or cycling?

For roads, most highway standards limit grades to 6-8% on major routes and up to 12% on local streets. For cycling, grades above 8% are considered challenging and above 15% are very difficult. Mountain roads such as alpine passes can reach 12-20%. Railways are engineered to much lower grades — typically under 2-3% — because steel wheels on steel rails have very low friction.

How is grade used in construction and accessibility standards?

In construction, ramp grades are tightly regulated. The Americans with Disabilities Act (ADA) and the UK Approved Document M both specify that accessible ramps must not exceed 1:12 (8.33% grade, about 4.76 degrees). Footpaths are generally limited to 5% (1:20). Driveway grades are typically kept under 15-20% for safe vehicle access in wet conditions.

Elevation Grade Calculator

The elevation grade calculator converts between every common way of expressing slope steepness — percent grade, decimal ratio, permille, angle in degrees and slope distance — and lets you solve for any one of them given the others. Whether you are designing a ramp, planning a cycle route, reading a topographic map, or checking building-regulations compliance, you get the full picture in one place.

How it works

Slope is fundamentally the relationship between vertical change (rise) and horizontal distance (run). From those two numbers every other representation follows directly:

Grade (%) = (Rise / Run) x 100

Angle = arctan(Rise / Run) expressed in degrees

Slope distance = sqrt(Rise squared + Run squared)

The calculator exposes four modes:

Solve for grade — enter rise and run, get grade in your chosen unit (%, ratio or ‰).
Solve for rise — enter grade and run, get the vertical change.
Solve for run — enter grade and rise, get the horizontal distance.
Solve for angle — enter grade in any unit, get the equivalent angle in degrees.

A summary panel always shows all four representations simultaneously so you can cross-check without switching modes.

Worked example

A wheelchair ramp must rise 0.6 m to reach a doorstep. You have 7 m of horizontal space.

Grade = (0.6 / 7) x 100 = 8.57 %
Angle = arctan(0.6 / 7) x (180 / pi) = 4.9 degrees
Slope distance = sqrt(0.6 squared + 7 squared) = 7.026 m

The 8.57% grade exceeds the ADA/Doc M limit of 8.33% (1:12). You would need at least 7.2 m of run to be compliant — enter that in the “Solve for run” mode with grade set to 8.33% and rise 0.6 m to confirm.

Rise	Run	Grade	Angle
1 m	20 m	5%	2.86 deg
1 m	12 m	8.33%	4.76 deg
1 m	10 m	10%	5.71 deg
1 m	5 m	20%	11.31 deg
1 m	1 m	100%	45 deg

Formula notes

Percent and degrees are not proportional. A 45-degree slope equals exactly 100% grade, and beyond 45 degrees the grade exceeds 100%. Road engineers work in percent because small percentages are easier to read on signage and to specify in contracts. Surveyors and geographers prefer degrees or radians. Railway engineers often use permille (‰) because their grades are so gentle — a 10 ‰ (1%) railway climb is considered significant. All conversions here are exact to floating-point precision.