My Python code does math.sin(45) and gets 0.85 instead of 0.707. What's wrong?

Python's math.sin() takes radians. math.sin(45) calculates the sine of 45 radians, not 45°. Convert first: math.sin(45 × math.pi / 180) = math.sin(0.7854) ≈ 0.7071.

I'm setting up a stepper motor controller that takes position in radians. My mechanical drawing shows 37.5°. What do I enter?

37.5 × (π / 180) = 37.5 × 0.017453 ≈ 0.6545 radians. Enter 0.6545.

Why do scientists use radians instead of degrees?

Radians make calculus clean. The derivative of sin(x) is cos(x) only when x is in radians. If you use degrees, an extra factor of π/180 appears in every derivative and integral. Physics and mathematics chose radians to keep formulas simple.

What are the key degree-to-radian values worth memorizing?

30° = π/6 ≈ 0.524, 45° = π/4 ≈ 0.785, 60° = π/3 ≈ 1.047, 90° = π/2 ≈ 1.571, 180° = π ≈ 3.142, 270° = 3π/2 ≈ 4.712, 360° = 2π ≈ 6.283.

Degrees to Radians Converter

Enter a value to instantly convert between angle units.

From

Precision4 dp

1 Degree = 0.0175 Radian

Key Formulas

Degree → Radian

rad = ° × 0.0174533

Radian → Degree

° = rad × 57.2958

Degree → Gradian

grad = ° × 1.11111

Gradian → Degree

° = grad × 0.9

Formula

radians = degrees × (π ÷ 180)

Every programming language's math library — Python's math.sin(), JavaScript's Math.cos(), C's sin() — takes angles in radians. An engineer who models a 30° slope in Excel uses degrees, but feeding that slope into a simulation or a CAD API requires radians. Robotics joint angles are specified in degrees in datasheets but controlled in radians by the firmware. The conversion is the bridge between human-readable angle specs and machine-executable math.

Source: ISO 80000-3:2019 (Quantities and units — Space and time)

Last reviewed: 2026-06-11 · see our methodology

Frequently Asked Questions

Real-World Examples

A 30° roof pitch — the radian value used in a structural calculation for snow load (force per unit area on a sloped surface).

30 ° = 0.5236 rad

A 45° camera pan angle — the radian argument passed to a 3D rotation matrix in a game engine or animation software.

45 ° = 0.7854 rad

A right-angle servo position — π/2 radians, the target angle sent to a robot arm's joint controller in ROS.

90 ° = 1.5708 rad

A full U-turn — π radians, the value used in a navigation algorithm to reverse the heading of an autonomous vehicle.

180 ° = 3.1416 rad

radians to degrees degrees to gradians gradians to degrees

Degrees to Radians Converter

Key Formulas

Formula

Frequently Asked Questions

Real-World Examples

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