About

In construction and roofing, specifying a gradient often involves mixing units: a vertical rise in millimeters (mm) over a horizontal run in meters (m). For example, a "flat" roof might fall 20 mm for every 1 meter. To determine if this meets code or design specifications, you need to convert this linear ratio into an angular Degree (°).

This calculator performs the trigonometric conversion using the arc-tangent function. It requires two inputs: the vertical Rise (mm) and the horizontal Base/Run (m). The default Run is set to 1 meter, making it easy to calculate "mm per meter" slopes instantly. The tool outputs both the angle in degrees and the grade in percentage (%).

Formulas

The calculation uses the trigonometric Inverse Tangent (arctan) function. Since the inputs are in different units (mm vs m), the Run must first be normalized to mm.

θ = arctanRise_mmRun_m × 1000 × 180π

For Percentage Grade:

Grade_% = Rise_mmRun_m × 1000 × 100

Reference Data

Rise (mm per 1m run)	Angle (Degrees)	Gradient (%)	Common Application
10 mm	0.57°	1.0%	Drainage Min.
20 mm	1.15°	2.0%	Flat Roofs / Terraces
50 mm	2.86°	5.0%	Wheelchair Ramps (Max 1:20)
83 mm	4.76°	8.3%	Ramp Standard (1:12)
100 mm	5.71°	10.0%	Steep Driveways
250 mm	14.04°	25.0%	Low Pitch Roof
500 mm	26.57°	50.0%	Standard Gable Roof
1,000 mm (1m)	45.00°	100.0%	45 Degree Pitch (12/12)

Frequently Asked Questions

An angle cannot be determined by a single length (mm) alone. You need to know the horizontal distance over which that rise occurs. Standard slope notation is often "mm per 1 meter", hence the default run of 1m.

While codes vary, a common minimum is a 1:80 (12.5mm per meter) or 1:40 (25mm per meter) slope to ensure adequate drainage and prevent ponding.

This tool does it automatically. Mathematically, Degrees = arctan(Percent / 100). For small angles, 1% is roughly 0.57 degrees.

Yes. Plumbers often use "fall per meter". For example, a 20mm fall over 1m run is a 2% grade, ideal for sewage pipes to maintain self-cleansing velocity.