About

Precision engineering and construction often require translating an angular specification into a linear dimension. For a machinist setting a compound slide on a lathe, or a builder checking a floor slope, an angle in degrees is abstract until converted into millimeters of deviation over a known distance. This tool solves the "Right Triangle" problem instantaneously.

By inputting the Angle and the Base Length, you determine the precise Height (or Taper). This is critical in taper turning where even a 0.1° error can ruin a workpiece. The tool handles the trigonometric tangent function and alerts users to physical impossibilities (like 90° vertical walls having infinite slope).

Formulas

The calculation uses the tangent trigonometric function. Given an angle θ and a base length L, the height deviation H is:

H = L × tanθ

For Reverse Mode (finding the angle from dimensions):

θ = arctanHL

Reference Data

Angle (°)	Taper per 100mm	Taper per Meter (1000mm)	Common Application
0.5°	0.87 mm	8.73 mm	Drainage Slope
1.0°	1.75 mm	17.46 mm	Standard Road Camber
2.86°	5.00 mm	50.00 mm	1:20 Ratio
5.0°	8.75 mm	87.49 mm	Wheelchair Ramp (Max)
10.0°	17.63 mm	176.33 mm	Steep Driveway
15.0°	26.79 mm	267.95 mm	Machine Taper (Steep)
30.0°	57.74 mm	577.35 mm	Roof Pitch
45.0°	100.00 mm	1000.00 mm	1:1 Slope

Frequently Asked Questions

At 90 degrees, the tangent function is undefined (infinite). Physically, this represents a vertical wall where the height deviation is infinite relative to the base.

The math is identical, but the units differ. If you input length in feet, the result is in feet. To get Taper per Foot in inches, input "12" as the length.

No. This tool calculates the "Opposite" side (Height/Rise). If you need the diagonal length (Hypotenuse), you would need to use the cosine function or Pythagorean theorem.

In machining, parts often fit together with high tolerances. A small angular deviation translates to a gap or interference fit over the length of the part.