Inches to Degrees Calculator

Convert linear measurements to angular degrees. Enter the arc length and radius to calculate the corresponding angle.

Geometry Calculator:

Converts inches to degrees using arc length formula. Essential for pipe bending, circular layouts, and angular measurements in construction.

Inches to Degrees Converter

Mode

Linear distance along the curve

Distance from center to edge of the circle

1 Radius (inches) 100

Calculation Results

Enter arc length and radius

then click "Calculate" for angle

Inches to Degrees: A Practical Guide

Converting inches to degrees isn't a straightforward swap like changing feet to meters. These units measure different things—inches measure length, while degrees measure angles. The connection between them comes through circular geometry, specifically the relationship between arc length and the radius of a circle.

The Formula Behind the Calculation

Primary Formula
Degrees = (Arc Length × 57.2958) ÷ Radius
The constant 57.2958 comes from 180 ÷ π, converting radians to degrees.
Full Mathematical Form
θ = (Arc Length ÷ 2πr) × 360
Where θ is the angle in degrees, and r is the radius in the same unit as arc length.

Example Calculation Table

Arc Length (in) Radius (in) Angle (degrees) Angle (radians)
5 10 28.65° 0.50 rad
10 20 28.65° 0.50 rad
12 15 45.84° 0.80 rad
20 25 45.84° 0.80 rad
15.71 10 90.00° 1.57 rad
31.42 10 180.00° 3.14 rad