Skip to main content

Polar Coordinates Calculator

Math Calculators

Convert between polar (r, θ) and Cartesian (x, y)

Quick Answer

Polar Coordinates Calculator: Convert between polar (r, θ) and Cartesian (x, y). Polar Coordinates Calculator uses standard math formulas to compute accurate results instantly.

Conversion mode

x = r·cos θ4.3301
y = r·sin θ2.5
(x, y)(4.3301, 2.5)

Steps

  1. 1x = r·cos θ = 5 × cos(30°) = 4.3301
  2. 2y = r·sin θ = 5 × sin(30°) = 2.5
  • Formulas: x = r·cos θ, y = r·sin θ; r = √(x² + y²), θ = atan2(y, x).
  • atan2 returns the principal angle in (−180°, 180°]; add 360° when negative to get the [0°, 360°) equivalent.
  • At the origin r = 0 the angle is undefined; a negative r flips the direction: (−r, θ) = (r, θ + 180°).

Was this tool helpful?

How to Use

  1. Enter values or expressions: type directly into the Polar Coordinates Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Polar Coordinates Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Convert between polar (r, θ) and Cartesian (x, y).
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Polar Coordinates Calculator formula

Polar Coordinates Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Polar Coordinates Calculator?
Open the page and fill in the input fields — results update automatically. Convert between polar (r, θ) and Cartesian (x, y).
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

Related Tools

Related Guides

Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Polar Coordinates Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/polar-coordinates

Results provided by this tool are for reference only and do not constitute professional advice.