Convert rectangular (x, y) to polar (r, θ) coordinates in degrees, radians, or gradians. Quadrant detection, batch mode, visual plot, and reference table.
The **Rectangular to Polar Calculator** converts Cartesian coordinates (x, y) to polar form (r, θ) with support for degrees, radians, and gradians. It computes the radius r = √(x² + y²) and the angle θ = atan2(y, x), normalizing the result to the [0°, 360°) range.
Every conversion displays all three angle units simultaneously so you never need to convert between systems manually. The calculator identifies which quadrant — or axis — the point lies in and displays a clean SVG coordinate plot showing the point, the radius line, and the angle arc. A quadrant sign-reference table highlights the current quadrant, making it easy to verify that signs and ranges are correct.
A batch conversion mode lets you convert multiple (x, y) pairs at once. Enter one pair per line, separated by commas, and the tool generates a complete table of polar coordinates. This is ideal for converting data sets or checking homework problems quickly.
The common conversions reference table lists the most frequently encountered coordinate pairs — unit-circle points at 0°, 30°, 45°, 60°, 90°, 180°, 270°, and classic Pythagorean pairs like (3, 4) and (5, 12). Eight preset buttons let you load test points in one click. Adjustable decimal precision from 0 to 10 places rounds every output consistently.
Rectangular to Polar Coordinates Calculator helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like r (radius), θ (degrees), θ (radians) in one pass.
r = √(x² + y²). θ = atan2(y, x), normalized to [0°, 360°). Radians: θ_rad = θ° × π/180. Gradians: θ_grad = θ° × 10/9.
Result: r = 5, θ ≈ 53.13°, θ ≈ 0.9273 rad
Using x=3, y=4, the calculator returns r = 5, θ ≈ 53.13°, θ ≈ 0.9273 rad. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to rectangular to polar coordinates calculator workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
atan2(y, x) is a two-argument arctangent function that returns the angle in the correct quadrant, unlike atan(y/x) which cannot distinguish between opposite quadrants. It returns values in (−π, π].
Use x = r·cos(θ) and y = r·sin(θ). CalcBee has a dedicated Polar to Rectangular calculator for this.
Gradians (also called gons) divide a full circle into 400 parts instead of 360 degrees or 2π radians. A right angle is 100 gradians. They are used in some European surveying systems.
atan2 returns values in (−π, π], which means negative angles for y < 0. Normalizing to [0°, 360°) provides a single, unambiguous representation for every direction.
Yes. A complex number z = x + yi can be written in polar form as z = r·(cos θ + i sin θ) = r·e^(iθ). The r computed here is the modulus |z| and θ is the argument.
At (0, 0), r = 0 and the angle θ is mathematically undefined. The calculator shows 0° by convention (the atan2 function returns 0 for this case).