Radians Calculator (rad, degrees, trig)
Use this rad calculator to convert between degrees and radians, normalize angles, and compute trigonometric values instantly.
pi/2.
What is a rad calculator?
A rad calculator is a tool that works with angles in radians. It usually converts values between radians and degrees, and often helps with trigonometric functions like sine, cosine, and tangent. Since many formulas in mathematics, physics, and programming are built around radians, this is one of the most useful quick calculators to keep nearby.
Radians vs degrees (quick understanding)
Why both units exist
Degrees are easy for everyday geometry because one full turn equals 360°. Radians are preferred in higher math because they are directly tied to circles and arc length. One full turn is 2π radians.
- 180° = π rad
- 90° = π/2 rad
- 45° = π/4 rad
- 360° = 2π rad
Core formulas used in this calculator
Degrees to radians
radians = degrees × (π / 180)
Radians to degrees
degrees = radians × (180 / π)
Arc and sector formulas (when radius is provided)
- Arc length: s = rθ
- Sector area: A = ½r²θ
In both formulas above, θ must be in radians.
How to use this rad calculator
- Type an angle (for example: 2.5, 90, pi/2, or 3pi/4).
- Select the unit of your input (radians or degrees).
- Optional: enter a radius if you also want arc length and sector area.
- Choose decimal precision and click Calculate.
Why radians are essential in real work
Calculus and higher mathematics
Derivative and integral identities in trigonometry are clean only when angles are in radians. For example, d/dx(sin x) = cos x assumes x is in radians.
Physics and engineering
Rotational motion, wave equations, and oscillations frequently use radians per second. Using degrees often requires extra conversion and can cause mistakes.
Programming and game development
Most programming language math libraries (like JavaScript’s Math.sin()) expect radians. A rad calculator helps prevent subtle bugs in animation, simulation, and graphics code.
Common input mistakes to avoid
- Mixing degrees and radians in the same formula.
- Using degree values directly in trig functions that expect radians.
- Forgetting to normalize angles when comparing rotations.
- Entering invalid pi notation (such as malformed fractions).
Practical examples
Example 1: Convert 120° to radians
120 × (π / 180) = 2π/3 ≈ 2.094395 rad
Example 2: Convert 2.2 rad to degrees
2.2 × (180 / π) ≈ 126.050715°
Example 3: Arc length
If radius r = 8 and angle θ = π/3 rad, then arc length is s = rθ = 8π/3 ≈ 8.37758.
Final note
This rad calculator is designed to be quick, practical, and accurate for classwork, engineering tasks, coding, and everyday trig conversion. Save it as a reference whenever you need a reliable degrees-to-radians converter and trig helper in one place.