Example 1
- Semi-axis a: 10
- Semi-axis b: 6
188.50
a = 10 and b = 6 gives 188.50.
Ellipse area calculator
Type both semi-axes. The calculator multiplies π by a and b and shows area in cm² or in². When a = b, the disk becomes a circle.
A = πab. A circle is on the area of a circle calculator. A rectangle is on the rectangle area calculator.
Result
Semi-axis a (cm) and Semi-axis b (cm). Area shows up here.
How it works
Ellipse area is π times both semi-axes. The first card example, 10 and 6, is 188.50, not 60 from the rectangle boxed by those axes. An older script without π showed exactly 60 and that was a bug.
The calculator multiplies π and does not leave a times b. A circle of r = 10 is 314.16; this ellipse is thinner.
When a = b the ellipse is a circle. Five and five give 78.54, the same as πr² at r = 5. Nine and nine give 254.47. A flat pair 4 and 1 gives 12.57, about 4π. Order of a and b does not matter. Semi-axes are half-diameters: a diameter of 20 means a = 10.
The calculator does not run when a semi-axis is missing. Typing diameters 20 and 12 as a and b inflates 188.50 four times, because both lengths enter linearly.
Switching to inches relabels the result as in² and does not convert a typed 10. Ellipse circumference, even a Ramanujan sketch, is not in this calculator.
At 8 and 3 you get 75.40. At 12 and 4 you get 150.80. At 15 and 5 you get 235.62. That is still πab, not paint on a 15 by 5 rectangle, which would be 75.
How to use
- Type semi-axis a, half the longer or shorter diameter, in cm or inches.
- Type semi-axis b in the same unit, the other semi-axis, perpendicular to a.
- Click Calculate. The result uses two decimal places and cm² or in².
- Do not expect a times b without π. That was an old-script bug, not the ellipse formula.
- The 10 and 6 example is 188.50. That is not 60 from a rectangle and not 314.16 from a circle of r = 10.
Formula
A = π × a × b
Not a × b without π.
A = πab at a = 10 and b = 6
π times both semi-axes. a = 10 and b = 6 give 188.50. When a = b = 5, the disk becomes a circle 78.54.
- A
- Area πab. 10 and 6 give 188.50. 8 and 3 give 75.40. Not a × b without π.
- a
- A semi-axis. 10 with b = 6 is 188.50. a = 5 and b = 5 is a circle of r = 5, area 78.54.
- b
- The other semi-axis. 6 with a = 10. 4 with a = 12 gives 150.80.
- π
- In the product with a and b. Without π you would keep 60 instead of 188.50 at 10 and 6.
Examples
Example 2
- Semi-axis a: 5
- Semi-axis b: 5
78.54
a = 5 and b = 5 gives 78.54, a circle of r = 5.
Example 3
- Semi-axis a: 8
- Semi-axis b: 3
75.40
a = 8 and b = 3 gives 75.40.
Example 4
- Semi-axis a: 12
- Semi-axis b: 4
150.80
a = 12 and b = 4 gives 150.80.
Example 5
- Semi-axis a: 7
- Semi-axis b: 2
43.98
a = 7 and b = 2 gives 43.98.
Example 6
- Semi-axis a: 9
- Semi-axis b: 9
254.47
a = 9 and b = 9 gives 254.47.
Example 7
- Semi-axis a: 4
- Semi-axis b: 1
12.57
a = 4 and b = 1 gives 12.57.
Example 8
- Semi-axis a: 15
- Semi-axis b: 5
235.62
a = 15 and b = 5 gives 235.62.
Frequently asked questions
Is ellipse area a times b without π?
No. That is a rectangle. An ellipse is πab. At 10 and 6 the rectangle is 60 and the ellipse is 188.50. The old script without π was a bug.
Why do 5 and 5 give 78.54?
Because a = b = r. π r squared at r = 5 is circle area 78.54. The ellipse becomes a circle.
Are 10 and 6 the same as a circle of r = 10?
No. A circle of r = 10 is 314.16. An ellipse 10 and 6 is 188.50. The second semi-axis thins the disk.
What if I leave b empty?
Nothing is computed. Type the second semi-axis or load 10 and 6. Empty b does not become a segment of length 2a.
Should I type diameters 20 and 12 instead of semi-axes?
No. Divide diameters by 2. Typing 20 and 12 as a and b inflates 188.50 four times.
Can I mix centimeters and inches?
Not in one run. Both semi-axes in cm or both in inches. The switch changes the label and does not convert numbers.
Is ellipse circumference here?
No. Only area πab. A Ramanujan circumference sketch lives on another page, not this one.
Why do 4 and 1 give 12.57?
To show a very flat ellipse. 4π is about 12.57. The formula does not need a close to b.
Do 5 and 5 give 78.57 from school 22/7?
No. The calculator multiplies π by 25. At a = b = 5 you get 78.54, the same as circle area at r = 5.
Is 8 and 3 equal to 75.40?
Yes. 24 times π rounds to 75.40. At 15 and 5 you get 235.62.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.