Road grade (or gradient) is the ratio of vertical rise to horizontal run, expressed as a percentage: Grade (%) = (Vertical Rise / Horizontal Run) × 100. A 6% grade rises 6 units vertically for every 100 units of horizontal travel.

Does road grade use horizontal run or traveled slope distance?

Standard civil surveying and highway engineering (FHWA) define grade using horizontal map projection (run), not the inclined hypotenuse (slope distance). Slope distance is computed via the Pythagorean theorem: √(Rise² + Run²).

How do you convert grade percentage to degrees?

Slope angle θ in degrees is the arctangent of the decimal slope: θ = arctan(Grade / 100) × (180 / π). For example, a 10% grade is arctan(0.10) ≈ 5.71°.

How is slope ratio (1:n) defined?

A slope ratio of 1:n expresses 1 unit of vertical rise for every n units of horizontal run. For example, an 8.333% grade equals 1:12, and a 1% grade equals 1:100.

How steep is a 6% grade?

A 6% grade rises or drops 6 ft per 100 ft of horizontal distance: an angle of 3.43°, a ratio of 1:16.7, or 316.8 ft per mile (60 m per km). A "6% grade next 5 miles" sign therefore means roughly 1,580 ft of descent.

How do I calculate grade from elevation and miles?

Convert both to the same unit and divide: grade % = elevation change ÷ (miles × 5,280) × 100. A road that climbs 1,000 ft in 3 miles averages 1,000 ÷ 15,840 × 100 = 6.31% (3.61°). If the 3 miles were measured along the road, the horizontal run is √(15,840² − 1,000²) = 15,808 ft and the grade is 6.33%, a negligible difference below about 15%.

What is the maximum grade for highways and interstates?

AASHTO's Green Book, as reproduced in state design manuals such as TxDOT's, limits freeways to 3–4% in level terrain and 4–5% in rolling terrain, with lower values at higher design speeds. Rural arterials allow 3–6%, collectors 5–10% and local roads 5–12% in level to rolling terrain. Mountainous terrain allows steeper grades, and short one-way downgrades under 500 ft may be 1% steeper.

Is a 100% grade vertical?

No. A 100% grade means the rise equals the run, which is a 45° slope. A vertical wall would be an infinite grade. That is why grade percent and degrees diverge quickly above about 10%: 20% is 11.3°, 50% is 26.6°.

Does this calculator determine ADA compliance?

No. The U.S. Access Board specifies a maximum 1:20 running slope for accessible-route walking surfaces and 1:12 for ramps governed by section 405, but full compliance also depends on other requirements. Use the official standard and applicable local rules.

Road Grade Calculator

Calculate grade percent, angle, elevation change, slope length, and gradient ratio (1:n); convert % ↔ degrees ↔ ratio ↔ ft per mile; and get the average grade from two elevations and a road distance.

Slope Parameters

Select your known pair to calculate vertical grade, angle, ratio, and distance.

Calculation Mode

Linear Distance Units

Vertical Rise / Drop

units

Horizontal Run

units

Calculated Grade & Alignment

Enter your slope parameters and click Calculate.

Slope conversion examples

Specification / Context	Grade (%)	Angle (°)	Ratio (1:n)
1:100 Civil Grade Base	1.000%	0.573°	1 : 100
ADA Accessible Route Max (walking surface)	5.000%	2.862°	1 : 20
ADA Section 405 Ramp Max Running Slope	8.333%	4.764°	1 : 12
10% Gradient Benchmark	10.000%	5.711°	1 : 10
45° Incline (1:1 Slope)	100.000%	45.000°	1 : 1

Grade uses horizontal run, not slope length. The ratio reports absolute steepness; the signed result separately identifies uphill or downhill. A slope value alone does not establish legal or design compliance.

ADA standards U.S. Access Board ramp guide FHWA Bridge Geometry Manual

Quick slope converter

Type in any box; the others update. Ratio is 1 vertical : n horizontal.

Grade (%)

Angle (°)

Ratio 1 : n

Feet per mile

Meters per km

Inches per foot

Average grade from elevations

For a road or trail segment: two elevations from a map, GPS or sign, and the distance between them.

Start elevation

End elevation

Elevation unit

Distance

Distance is measured

Average grade—

Angle · ratio—

Climb rate—

Grade percent to degrees conversion table

Grade	Degrees	Ratio 1 : n	ft / mile	m / km
0.5%	0.29°	1 : 200	26.4	5
1%	0.57°	1 : 100	52.8	10
2%	1.15°	1 : 50	105.6	20
3%	1.72°	1 : 33.33	158.4	30
4%	2.29°	1 : 25	211.2	40
5%	2.86°	1 : 20	264.0	50
6%	3.43°	1 : 16.67	316.8	60
7%	4.00°	1 : 14.29	369.6	70
8%	4.57°	1 : 12.5	422.4	80
8.333%	4.76°	1 : 12	440.0	83.33
9%	5.14°	1 : 11.11	475.2	90
10%	5.71°	1 : 10	528.0	100
12%	6.84°	1 : 8.33	633.6	120
15%	8.53°	1 : 6.67	792.0	150
20%	11.31°	1 : 5	1,056.0	200
25%	14.04°	1 : 4	1,320.0	250
30%	16.70°	1 : 3.33	1,584.0	300
50%	26.57°	1 : 2	2,640.0	500
100%	45.00°	1 : 1	5,280.0	1,000

Degrees = arctan(grade ÷ 100). Feet per mile = grade ÷ 100 × 5,280. 8.333% is the 1:12 ADA ramp limit.

Maximum road grades (AASHTO Green Book)

Rural road class	Design speeds	Level terrain	Rolling terrain
Freeway / Interstate	50–80 mph	3–4%	4–5%
Arterial	40–80 mph	3–5%	4–6%
Collector	20–60 mph	5–7%	6–10%
Local road	15–60 mph	5–9%	6–12%

The lower number applies at the higher design speed. Values from AASHTO A Policy on Geometric Design of Highways and Streets as reproduced in the TxDOT Roadway Design Manual, Table 4-11.
Mountainous terrain permits steeper grades; one-way downgrades shorter than 500 ft may be 1% steeper; very constrained local streets may reach about 15%.
Minimum grades for drainage: about 0.3% on curbed pavement and 0.5% in unlined roadside ditches.
Long grades are also limited by critical length: the distance a loaded truck can climb before slowing by about 10 mph.

Formulas and worked example

grade % = rise ÷ run × 100 · angle = arctan(rise ÷ run) · n = run ÷ rise · slope length = √(rise² + run²) · ft per mile = grade % × 52.8

A mountain pass climbs from 5,200 ft to 6,200 ft over 3 miles on the map. Rise = 1,000 ft, run = 3 × 5,280 = 15,840 ft, so the average grade is 1,000 ÷ 15,840 × 100 = 6.31%, an angle of 3.61°, a ratio of 1 : 15.84, and 333.3 ft per mile. Sections of the road will be steeper than the average.

Summary

How it works

Select your known calculation pair: rise & run, grade & run, angle & run, or rise & slope distance.
Choose your measurement unit (feet, meters, or generic units).
Enter positive numbers for uphill slopes or negative numbers for downhill slopes.
Click Calculate to compute grade percentage, slope angle, decimal slope, gradient ratio (1:n), and slope length.
Use the quick converter to turn any one of percent grade, degrees, 1:n ratio, feet per mile or meters per kilometer into the others.
Use the elevation card when you know the start and end elevations and the distance in miles or kilometers, measured on the map or along the road.
Use the linked official references when a design must meet a particular standard or local code.

Use cases

Calculate vertical road grade percentage from surveyed rise and horizontal map distance.
Convert slope angles in degrees to roadway grade percentages and gradient ratios.
Determine required horizontal run or vertical elevation change for site grading.
Convert traveled slope distance (hypotenuse) to true horizontal run for plan drawings.
Compare the geometry with a project-specific road, drainage, or accessibility requirement.
Determine slope ratios (e.g., 1:100, 1:20, 1:12) for drainage and civil engineering layouts.

Frequently Asked Questions

Last updated: 2026-10-09 · Reviewed by Nham Vu