Is a treadmill incline of 10 the same as 10 degrees?

No. Consumer and commercial treadmills display incline in percent grade, so a setting of 10 means a 10% slope — 10 m of rise per 100 m of horizontal run — which is an angle of only 5.71°. A true 10° tilt would be a 17.6% grade, beyond the maximum of most machines. The percent convention matches how road gradients are signed and how the ACSM metabolic equations expect incline to be entered.

Why is 45 degrees equal to 100% grade and not 45%?

Percent grade is the tangent of the angle times 100, and tan(45°) = 1, so rise equals run at exactly 100%. The two scales are not proportional: doubling the angle more than doubles the grade once slopes get steep. A 45% grade corresponds to 24.2°, and grades above 100% remain far from vertical — a 60° slope is a 173% grade, and the percent figure runs to infinity as the angle approaches 90°.

Can I just multiply percent grade by 0.57 to get degrees?

As a shortcut it holds up surprisingly well on shallow slopes. The small-angle approximation makes 1% ≈ 0.573°, so 10% estimates as 5.73° against a true 5.71°. By 20% the shortcut gives 11.46° against a true 11.31°, and at 45% it gives 25.8° against 24.2° — the error grows with steepness because the tangent curve bends away from linear. The converter applies the exact inverse tangent, so no approximation error is carried into the output.

Should grade be measured against horizontal distance or distance travelled?

The strict definition divides rise by horizontal run, which corresponds to the tangent of the slope angle. Many GPS devices and route profiles divide by distance along the slope instead, which corresponds to the sine and reads slightly lower. At typical road and treadmill grades the difference is a fraction of a percent of the value; on very steep trails it becomes noticeable — a 30% strict grade would read about 28.7% by the along-slope method.

What does the rise-to-run ratio in the output mean?

It expresses the slope as 1 unit of vertical rise per so many units of horizontal run — the notation used in building codes, ramp specifications, and railway engineering. A 10% grade is 1 : 10, meaning one metre up for every ten metres forward. Smaller second numbers mean steeper slopes: 1 : 6.7 for a 15% grade, 1 : 1 at 45°. The ratio carries the same information as percent grade, arranged for quick judgement of steepness.

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Conversions

Grade to Degrees Converter

Convert incline between percent grade and degrees, with rise-over-run shown both ways.

JCVerified Verified by Jobi Cheriyan, Founder & Builder

Updated 8 August 2026

What this tool does

This converter translates incline between its two common notations: percent grade (rise divided by horizontal run, times 100) and degrees of angle. Enter a grade to get the angle via degrees = atan(grade ÷ 100), or enter an angle — leave grade at 0 — to get the percent via grade = tan(angle) × 100. The result also reports the rise in metres per 100 m of horizontal run and the rise-to-run ratio. Treadmill incline displays, road signs, and trail gradients almost always use percent, while drawings and some equipment use degrees; the two scales are related through the tangent, not proportionally.

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Formula Used

θ = arctan (\frac{g}{100}), g = tan (θ) \times 100

θ

Slope angle in degrees

g

Percent grade

Disclaimer

This calculator is for educational and informational purposes only. It does not provide medical, nutritional, or training advice. Results are mathematical estimates and may not reflect individual circumstances. Consult a qualified coach, registered dietitian, medical professional, or physiotherapist for personal guidance.

Two notations for the same slope

An incline can be written as a percent grade or as an angle in degrees, and the two are linked by trigonometry rather than by a simple scaling. Percent grade is rise divided by horizontal run, multiplied by 100: climb 10 m over 100 m of horizontal travel and the grade is 10%. The angle of that same slope is atan(10 ÷ 100) = 5.71°. Going the other way, a slope of known angle has grade = tan(angle) × 100. The distinction matters because the tangent is only approximately linear at small angles — the shortcut "1% ≈ 0.57°" works well below about 20% grade and drifts increasingly thereafter.

Worked examples in both directions

From grade to degrees: a 15% grade gives atan(0.15) = 8.53°. The rise-over-run reading is direct — 15 m of rise per 100 m of run, a ratio of 1 : 6.7. From degrees to grade: a ramp drawn at 5° has grade tan(5°) × 100 = 8.7%, rising 8.7 m per 100 m of run, a ratio of 1 : 11.4. Note the asymmetry in effort of interpretation: percent grade reads straight off a map or elevation profile (vertical gain ÷ horizontal distance), while degrees require the inverse tangent every time.

Treadmill "incline 10" is percent, not degrees

Treadmill incline displays are calibrated in percent grade. Setting the machine to 10 tilts the deck to a 10% slope — 5.71° of actual angle — not to 10°. A 10° deck would be a 17.6% grade, steeper than almost any consumer treadmill reaches. The percent convention carries into the exercise-science literature: the ACSM walking and running equations take fractional grade (10% entered as 0.10) as their incline term, and published treadmill test protocols such as the Bruce protocol specify stages in percent. The treadmill pace tool and the elevation pace tool on this site both follow the same percent convention.

The 45° confusion

A persistent misreading is to treat the two scales as meeting at 100: they do not. A 45° slope is a 100% grade — rise equals run — not a 45% grade. A 45% grade is only 24.2°. And a 100% grade is very far from a vertical wall; vertical is 90°, where the tangent, and therefore percent grade, goes to infinity. This is why extremely steep pitches are quoted in degrees rather than percent: a 60° face would be a 173% grade, a figure nobody uses. The converter caps its degree input at 45° because beyond that point percent notation stops being informative.

Common treadmill settings converted

Grade (%)	Degrees	Rise per 100 m run
1	0.57°	1 m
2	1.15°	2 m
4	2.29°	4 m
6	3.43°	6 m
8	4.57°	8 m
10	5.71°	10 m
12	6.84°	12 m
15	8.53°	15 m
20	11.31°	20 m
25	14.04°	25 m

The 1% row is the setting commonly cited in the literature as approximating the air-resistance cost of outdoor running that a treadmill otherwise removes.

One technical footnote: run versus distance travelled

Percent grade divides rise by horizontal run. Elevation profiles and GPS devices often divide by distance travelled along the slope instead, which understates the grade slightly — sin versus tan of the angle. At 10% the difference is about 0.5% of the value; at 30% it approaches 4%. For treadmill settings and road gradients the discrepancy is negligible, but it explains small mismatches between a mapped gradient and one computed from rise over track distance on steep trails.

Questions

Is a treadmill incline of 10 the same as 10 degrees?: No. Consumer and commercial treadmills display incline in percent grade, so a setting of 10 means a 10% slope — 10 m of rise per 100 m of horizontal run — which is an angle of only 5.71°. A true 10° tilt would be a 17.6% grade, beyond the maximum of most machines. The percent convention matches how road gradients are signed and how the ACSM metabolic equations expect incline to be entered.
Why is 45 degrees equal to 100% grade and not 45%?: Percent grade is the tangent of the angle times 100, and tan(45°) = 1, so rise equals run at exactly 100%. The two scales are not proportional: doubling the angle more than doubles the grade once slopes get steep. A 45% grade corresponds to 24.2°, and grades above 100% remain far from vertical — a 60° slope is a 173% grade, and the percent figure runs to infinity as the angle approaches 90°.
Can I just multiply percent grade by 0.57 to get degrees?: As a shortcut it holds up surprisingly well on shallow slopes. The small-angle approximation makes 1% ≈ 0.573°, so 10% estimates as 5.73° against a true 5.71°. By 20% the shortcut gives 11.46° against a true 11.31°, and at 45% it gives 25.8° against 24.2° — the error grows with steepness because the tangent curve bends away from linear. The converter applies the exact inverse tangent, so no approximation error is carried into the output.
Should grade be measured against horizontal distance or distance travelled?: The strict definition divides rise by horizontal run, which corresponds to the tangent of the slope angle. Many GPS devices and route profiles divide by distance along the slope instead, which corresponds to the sine and reads slightly lower. At typical road and treadmill grades the difference is a fraction of a percent of the value; on very steep trails it becomes noticeable — a 30% strict grade would read about 28.7% by the along-slope method.
What does the rise-to-run ratio in the output mean?: It expresses the slope as 1 unit of vertical rise per so many units of horizontal run — the notation used in building codes, ramp specifications, and railway engineering. A 10% grade is 1 : 10, meaning one metre up for every ten metres forward. Smaller second numbers mean steeper slopes: 1 : 6.7 for a 15% grade, 1 : 1 at 45°. The ratio carries the same information as percent grade, arranged for quick judgement of steepness.

Sources & Methodology

Degrees = atan(grade ÷ 100) × 180 ÷ π, where grade is percent grade (rise ÷ horizontal run × 100). In the reverse direction, grade = tan(degrees × π ÷ 180) × 100. Rise per 100 m of horizontal run equals the percent grade read as metres; the rise-to-run ratio is 1 : (100 ÷ grade). A non-zero grade input takes precedence; a grade of 0 derives the conversion from the angle input.

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