Explore our free online polar function grapher, world's best polar function graphing calculator, easy-to-use and sophisticated.
What is a Polar Function Grapher?
A polar function grapher is a function grapher that draws the graph of a function in the polar coordinate system on its domain of definition. A function graph in the polar coordinate system is called the polar graph or polar curve of the function.
Features of Our Polar Function Grapher
- Animated Polar Graphs: Experience the most captivating polar graph animation. Our online polar function grapher uses a unique animation algorithm to visualize the step-by-step construction of polar graphs of functions. This makes it easy to see how even the most complicated polar graphs are created.
- Rotating Angular (Radial) Axes: In animating the construction of polar graphs, our online polar function graphing calculator is unmatched in its ability to rotate radial axes. This allows you to create stunning visualizations that help you understand the intricacies of polar graphing of functions.
- Seamless Switching Between Polar and Cartesian Graphs: Our polar function grapher makes it easy to switch between polar and Cartesian coordinate systems by checking/unchecking the Polar checkbox. This allows you to visualize the polar graph and Cartesian graph of a given functions in either coordinate system with remarkable ease.
How Our Polar Function Grapher Works
Our polar function grapher plots function graphs in the polar coordinate system in a similar way to how you would graph them on paper.
The polar function graphing calculator does this by drawing angular (radial) axes for the values of
θ that increase incrementally.
For each value of
θ a radial axis is drawn making an angle of
θ with the polar axis. The polar function graphing calculator calculates the signed distance
r(θ) and locates that point along the radial axis.
The polar function grapher then connects this point to the next point located using the same method with a slightly larger value of
θ. The online polar function graphing calculator thus completes the polar graph of the given function.
You can watch the entire polar graphing process by running the animation feature as described below.
Lines1 x+1 2x
Parabolasx^2 0.5x^2-4x+1 -(0.5x^2-4x+1)
Other graphs√(4sin(2x)) √(4cos(2x))
Lines2csc(θ) 2sec(θ) 1/(sin(θ) - cos(θ))
Circles1 2 6sin(θ) 8cos(θ)
Spiralsθ θ/5 dom=(0, 10π) √(θ) dom=(0, 10π) 1/θ dom=(0, 10π)
Roses4sin(3θ) 4sin(2θ) 4sin(5θ) 4sin(4θ)
Ellipses1/(1-.8cos(θ)) 1/(1-.8sin(θ)) 1/(1+.8cos(θ)) 1/(1+.8sin(θ))
Parabolas1/(1-sin(θ)) 1/(1+cos(θ)) 1/(1+sin(θ)) 1/(1-cos(θ))
Hyperbolas1/(1+2cos(θ)) 4/(1+2sin(θ)) 1/(1-2cos(θ)) 4/(1-2sin(θ))
Cardioids3+3cos(θ) 2+2sin(θ) 3-3cos(θ) 2-2sin(θ)
Limacons2+3cos(θ) 1+2sin(θ) 2-3cos(θ) 1-2sin(θ)
Butterfly curvee^sin(θ)-2cos(4θ)+sin((2θ-π)/24)^5 dom=(0, 12π)
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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the pop-up menu.
As you type:
- ..t is replaced by
θ. (You can also use
t; they are internally replaced by
- pi is replaced by
- inf (infinity) is replaced by