Basic Parameters

cm
cm
Semi-major axis must be greater than semi-minor axis.
Results
Area

188.50 cm²

Step 1: Use the area formula: A = π × a × b
Step 2: Plug in values: A = π × 10 × 6
Step 3: Calculate: A ≈ 188.50 cm²
Circumference

51.05 cm

Step 1: Use Ramanujan's approximation: C ≈ π[3(a + b) - √((3a + b)(a + 3b))]
Step 2: Plug in values: C ≈ π[3(10 + 6) - √((3×10 + 6)(10 + 3×6))]
Step 3: Calculate: C ≈ π[48 - √(36 × 28)] ≈ π[48 - √1008] ≈ π[48 - 31.749] ≈ 51.05 cm
Eccentricity

0.80

Step 1: Use the formula: e = √(1 - b²/a²)
Step 2: Plug in values: e = √(1 - 6²/10²) = √(1 - 36/100)
Step 3: Calculate: e = √(0.64) = 0.8
Focal Distance

8.00 cm

Step 1: Use the formula: f = √(a² - b²)
Step 2: Plug in values: f = √(10² - 6²) = √(100 - 36)
Step 3: Calculate: f = √64 = 8 cm
Latus Rectum

7.20 cm

Step 1: Use the formula: LR = 2b²/a
Step 2: Plug in values: LR = 2×6²/10 = 72/10
Step 3: Calculate: LR = 7.2 cm
Directrix

12.50 cm

Step 1: Use the formula: x = ±a²/f
Step 2: Plug in values: x = ±10²/8 = ±100/8
Step 3: Calculate: x ≈ ±12.5 cm

Detailed Calculations

Perform a calculation first to see detailed steps here.

Ellipse Visualization

Export Results

Export Data

Save your ellipse calculations in various formats.

Print Results

Generate a printer-friendly version of your results.

Interactive Guide

An ellipse is a closed curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.

In the diagram below, for any point P on the ellipse, PF₁ + PF₂ is constant.

Ellipse diagram

Semi-major axis (a): The longest radius of the ellipse, from center to the farthest point.

Semi-minor axis (b): The shortest radius of the ellipse, from center to the nearest point.

Focal points (F₁, F₂): Two fixed points inside the ellipse used in its definition.

Eccentricity (e): A measure of how much the ellipse deviates from being circular (0 = circle, 1 = parabola).

  • Area: A = πab
  • Circumference: C ≈ π[3(a + b) - √((3a + b)(a + 3b))] (Ramanujan's approximation)
  • Eccentricity: e = √(1 - (b²/a²))
  • Focal distance: f = √(a² - b²)
  • Latus rectum: LR = 2b²/a
  • Directrix: x = ±a²/f