Degrees ↔ Radians
Trigonometry
Intro: We detect units automatically and return exact forms (like 225° → 5π/4) and a decimal approximation.
Worked example
- Convert $225^{\circ}$ to radians.
- Conversion factor: $$1^{\circ} = \frac{\pi}{180}\ \text{radians}.$$
- Multiply by the factor: $$225^{\circ}\times\frac{\pi}{180^{\circ}} = \frac{225}{180}\pi.$$
- Reduce the fraction by $\gcd(225,180)=45$: $$\frac{225}{180}=\frac{225/45}{180/45}=\frac{5}{4}.$$
- Exact radian measure: $$\boxed{\tfrac{5\pi}{4}}.$$
- Decimal approximation (optional): $$\tfrac{5\pi}{4}\approx 3.92699\ \text{rad}.$$
- Convert $\tfrac{5\pi}{6}$ to degrees.
- Conversion factor: $$1\ \text{radian} = \frac{180^{\circ}}{\pi}.$$
- Multiply by the factor: $$\frac{5\pi}{6}\times\frac{180^{\circ}}{\pi} = \frac{5\cancel{\pi}}{6}\times\frac{180^{\circ}}{\cancel{\pi}}=\frac{5\cdot180^{\circ}}{6}.$$
- Compute: $$\frac{900^{\circ}}{6}=150^{\circ}.$$
- Exact degree measure: $$\boxed{150^{\circ}}.$$
- Decimal check (optional): $$\tfrac{5\pi}{6}\approx 2.61799\ \text{rad} \Rightarrow 2.61799\times\frac{180}{\pi}\approx150^{\circ}.$$
FAQs
Decimals?
We output both the exact \pi form and a decimal approximation (to ~5–6 significant figures).
Negative or large angles?
Same rules apply. You can also reduce modulo $360^{\circ}$ (or $2\pi$) if a principal value is desired.
How do I spot the unit?
We treat inputs with the ° symbol as degrees; otherwise, if the input contains \pi or looks radian-sized, we interpret it as radians.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
Deg↔Rad
- Multiply by π/180 and simplify the fraction (e.g., 225° × π/180 = 5π/4)
- Multiply by 180/π and cancel π (e.g., (5π/6) × 180/π = 150°)
- Evaluate the exact form numerically for a decimal approximation