Slope Percentage Calculator

Q: What does “1 in N” mean?

For every N units horizontally, the rise is 1 unit. % grade = 100/N.

Q: What about vertical (run = 0)?

Vertical implies undefined/infinite %, and θ = 90°. The calculator flags this case.

Compute road/grade slope % from rise & run — or convert between percent grade, angle (°), and ratio (1 in N). See clear steps, a right-triangle illustration, and a steepness gauge.

Background

By definition, slope % = (rise / run) × 100. The angle obeys θ = arctan(rise/run), and the common “1 in N” ratio means rise = 1 for run = N, so % = 100 / N.

Enter known values

Rise & Run (any length units):

Units cancel (e.g., meters with meters, feet with feet).

Percent grade:

If provided, we’ll use this directly (and ignore rise/run).

Angle (degrees):

Ratio “1 in N”:

1 in

Example: 1 in 20 → % grade = 100 / 20 = 5%.

Show:

Step-by-step working

Right-triangle illustration

Steepness gauge

Round to sensible significant figures

Quick picks:

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Result:

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How this calculator works

If you know rise & run: compute % = (rise/run) × 100.
If you know %: angle θ = arctan(% / 100), ratio N = 100 / %.
If you know θ: % = 100 · tan(θ), ratio N = 1 / tan(θ) (for positive slopes).
If you know 1 in N: % = 100 / N, θ = arctan(1/N).
Sign: A negative rise means downhill; the magnitude sets steepness.

Formula & Equation Used

Slope percent

% = 100 \frac{rise}{run}

Angle

θ = arctan (\frac{rise}{run})

θ = arctan (\frac{%}{100})

Ratio “1 in N”

% = \frac{100}{N}, N = \frac{100}{| % |}

Example Problem & Step-by-Step Solution

Example 1 — Rise 5 m over Run 100 m

% = 100 × (5 / 100) = 5%; θ = arctan(0.05) ≈ 2.862°; ratio ≈ 1 in 20.

Example 2 — 12% grade (given %)

Given % = 12.
Angle: θ = arctan(%/100) = arctan(12/100) ≈ 6.84°.
Ratio: N = 100/|%| = 100/12 ≈ 8.33 → 1 in 8.33.

Example 3 — θ = 30° (given angle)

% = 100 · tan(θ) = 100 · tan(30°) ≈ 100 · 0.57735 = 57.7%.
Ratio: N = 1/tan(θ) = 1/0.57735 ≈ 1.73 → 1 in 1.73.

Frequently Asked Questions

Q: Is 10% the same as 10 degrees?

No. 10% means tan(θ) = 0.10 ⇒ θ ≈ 5.71°.

Q: What does “1 in N” mean?

For every N units horizontally, the rise is 1 unit. % = 100/N.

Q: What about vertical (run = 0)?

That’s undefined/infinite % and θ = 90°. The calculator will flag it.