Radians in 60 seconds: arc, sector, and one calculator toggle

Published 2026-04-29 · Written by Pete Bromfield

Two formulas, one calculator toggle, and you own every P2 radian question. Here's the whole thing.

The formulas

• Arc length: $s = r\theta$.
• Sector area: $A = \tfrac{1}{2} r^2 \theta$.

Both need $\theta$ in radians. Always.

The calculator trap

If your calculator is in DEGREES when you compute $\sin(0.5)$, you'll get $\sin(0.5°) \approx 0.00873$ — which is massively different from $\sin(0.5\text{ rad}) \approx 0.479$. Every year students lose 3 marks in Paper 1 on this. Always check the mode indicator (usually a small R or D in the top-right of the screen).

Worked example

A sector has radius 6 cm and angle $0.7$ radians. Find its arc length and area.

• Arc: $6 \cdot 0.7 = 4.2$ cm.
• Area: $\tfrac{1}{2} \cdot 36 \cdot 0.7 = 12.6$ cm².

Not sure your calculator's in the right mode? Check the calculator guide for the exact button-press per model.