Polar Grapher
Plot polar curves r(θ)
About this calculator
The Polar Grapher plots a polar curve r(θ) over a chosen angle range and reports its maximum radius, the swept sector area (½∫r²dθ) and the arc length (∫√(r²+r'²)dθ). Type expressions like 1 + cos(theta), cos(2*theta), or 2 using theta as the angle in radians.
How to use the Polar Grapher calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- Cardioid r = 1 + cos(theta) over [0, 2π] → max radius 2, area ≈ 4.7124 (3π/2), arc length 8
- Four-petal rose r = cos(2*theta) → area ≈ 1.5708 (π/2), arc length ≈ 9.6884
- Circle r = 2 → area ≈ 12.566 (4π), circumference ≈ 12.566
- Spiral r = theta over [0, 2π] → max radius ≈ 6.2832, arc length ≈ 21.256
Frequently asked questions
How does the Polar Grapher calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Polar Grapher calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.