Cartesian to Polar

The Cartesian to Polar computes r from 2 inputs: x, y. Convert (x, y) to polar (r, θ).

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Cartesian to Polar sits in that toolkit — it convert (x, y) to polar (r, θ). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

x

x

y

y

r

Output value

θ (°)

Output value

1. 01Start by noting the input — x: 3.
2. 02Start by noting the input — y: 4.
3. 03Substitute these values into the formula: r = √(t²+a²) | θ (°) = 180 × atan2(a,t) / π
4. 04Compute r: the calculator returns 5.
5. 05Compute θ (°): the calculator returns 53.1301.
6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.