Slope / Grade Converter (Percent ↔ Degrees ↔ Rise:Run)
A single ramp can be described three ways: (1) percent grade — rise ÷ run × 100 % (8 % means 8 m rise per 100 m horizontal run); (2) angle — arctan(rise ÷ run), expressed in degrees; (3) ratio — "1 : N" reads as "rise 1 unit over a run of N units". This tool converts in all three directions and also surfaces radians and the rise / run pair. Use negative values for downhill.
Enter a valid number. Angles must satisfy −90° < θ < 90°.
Percent grade
10.0000%
Given
Degrees
5.7106°
Computed
Ratio 1 : N
1 : 10
Computed
Angle in radians
0.0997
For every 1 unit of rise, how much horizontal run?
1 m / 10 m
Formulas
G(%) = (rise/run) × 100; θ = arctan(G/100); 1 : N → G = 100 / N
Road signs and highway design typically quote percent grade (5% = 5 m rise per 100 m). Hiking and cycling use percent or degrees. Accessibility ramps and roof pitch are usually given as a 1 : N ratio (ADA caps an accessible ramp at 1 : 12 ≈ 8.33% ≈ 4.76°). Negative values mean downhill. This tool converts freely between all three forms and also shows radians and the rise/run pair.
Formula
G(%) = (rise / run) × 100 θ° = arctan(rise / run) = arctan(G / 100) 1:N → G(%) = 100 / N G(%) → 1:N = 1 : (100 / G)
- · Quick reference: 1 % = 0.5729°; 5 % = 2.862°; 8.33 % ≈ 4.764° ≈ 1 : 12 (US ADA max ramp); 10 % = 5.711° ≈ 1 : 10; 15 % = 8.531° ≈ 1 : 6.67; 20 % = 11.31° ≈ 1 : 5; 45° = 100 % = 1 : 1.
- · Roads: Europe and the US sign grades in percent. The AASHTO Green Book caps US interstates near ~6 %. European mountain roads (Stelvio, Mortirolo) reach 18–25 % at the steepest ramps.
- · Accessibility: ADA Standards §405 limits an accessible ramp to 1 : 12 (≈ 8.33 %). BS 8300-1:2018 (UK) and ISO 21542:2011 use similar caps with even gentler defaults.
- · Roof pitch: North America uses "rise / 12" notation (6 / 12 = 6 in rise per 12 in run = 1 : 2 = 50 % = 26.57°). Europe and most of Asia use degrees or percent. Minimum drainage pitch is typically 1 : 40 ≈ 2.5 % for asphalt or sheet metal.
- · Cycling: 5 % is "gentle"; 8–10 % "noticeable climb"; 12–15 % "steep"; 20 %+ "very steep". Strava and TrainingPeaks display gradient in percent by default.
- · References: AASHTO Green Book (2018) Table 3-5; UK DfT DMRB CD 109; ADA Standards (2010) §405; BS 8300-1:2018; International Roofing Code §1507.
Frequently asked
Which is steeper: an 8 % grade or an 8° angle?
8° is significantly steeper than 8 %. An 8 % grade means rise / run = 0.08, so angle = arctan(0.08) ≈ 4.574°. Conversely 8° corresponds to grade = tan(8°) × 100 ≈ 14.05 %. The two are close for small slopes (5 % ≈ 2.86°) but diverge quickly. Road signs, hiking and cycling apps tend to use percent (unitless, linear, easy mental math); surveys, technical drawings and accessibility standards prefer degrees or 1 : N. Mixing them up can almost double your perceived slope.
Why is 1 : 12 such a famous ramp slope?
The US ADA Standards §405 cap the slope of an accessible public ramp at 1 : 12 (≈ 8.33 % ≈ 4.764°), meaning every 1 unit of rise needs 12 units of horizontal run. The cap is set so that a person in a manual wheelchair can self-propel up the ramp without excessive strain, and rest landings must be added every 30 in of cumulative rise. The UK (BS 8300-1:2018), ISO 21542:2011 and Hong Kong's Buildings Department barrier-free guidelines all converge on the same neighbourhood, with some defaulting to a gentler 1 : 14 or 1 : 16. When designing new buildings, "1 : 12" is the number to remember.
What does a US "6/12 roof pitch" mean in degrees?
A "6/12 pitch" reads as "6 in of rise per 12 in of horizontal run" — rise/run = 0.5, which is a 50 % grade, an angle of arctan(0.5) ≈ 26.565° and a 1 : 2 ratio. North American roof categories: low-pitch 2/12 to 4/12 (9.46°–18.43°), standard 4/12 to 9/12 (18.43°–36.87°), steep 9/12 to 12/12 (36.87°–45°). Europe and most of Asia quote pitch directly in degrees ("a 30° roof"). To work back to a degree value enter 50 in percent mode (or 26.565 in degrees mode) in this tool.
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