Hubs:
Top Tools:
Math • Rectangular to Polar Coordinates Calculator

Rectangular to Polar Coordinates Calculator

Convert rectangular (Cartesian) coordinates (x, y) to polar coordinates (r, θ).

Radius (r = √(x² + y²))
5.0000
Angle (θ = atan2(y, x))
53.130°
Be the first person to rate this calculator
AdvertisementIn-Article
Calculation Guide & Reference

Rectangular (Cartesian) to Polar Coordinate Conversion Mathematics

Rectangular to polar calculator converts Cartesian coordinates (x, y) to polar coordinates (r, θ), computing radius and angle.

Standardized Mathematical Formula
r = √(x² + y²) | θ = atan2(y, x)

Polar coordinates describe a point by its distance from the origin (r) and angle from the positive x-axis (θ), rather than by horizontal/vertical offsets. The radius comes directly from the Pythagorean theorem; the angle uses the two-argument arctangent (atan2) to correctly handle all four quadrants.

Variables:
x, y:Rectangular (Cartesian) coordinates
r:Polar radius — distance from the origin
θ:Polar angle from the positive x-axis
How It Works (Step-by-Step)
  • 1Enter the x and y coordinates of a point.
  • 2View the equivalent polar radius (r) and angle (θ) in degrees.
Real-World Numerical Example
The Point (3, 4)

Convert the rectangular point (3, 4) into polar coordinates.

•r = √(3² + 4²) = √25 = 5.
•θ = atan2(4, 3) ≈ 53.13°.
Result: The point (3, 4) in polar coordinates is (r = 5, θ ≈ 53.13°).
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Regular arctan(y/x) only returns values between -90° and 90°, so it can't tell (3,4) apart from (-3,-4) — atan2(y,x) uses the signs of both x and y separately to correctly determine which of the four quadrants the point is in.

Use x = r × cos(θ) and y = r × sin(θ) — the reverse transformation.

Explore90 MathCalculators

Algebraic solvers, geometric area & volume, matrix operations, prime factorization, and percentages.

More in Math

Top Similar Tools (Math)

Tags:
Looking for More Calculators?

Explore more tools in Math (83+ more calculators available)

Browse our complete directory with category filters, formulas, and verified engines.