Aperture Area Calculator
This calculator works out the area of any circular aperture, the kind of opening you find in camera lenses, telescopes, pipes, or any round hole where the cross-sectional area matters more than the diameter alone. Choose your input method: enter a diameter directly, enter a radius directly, or switch to optics mode and enter a focal length together with an f-number so the calculator first derives the effective aperture diameter (focal length divided by f-number) before finding its area. You can set the input unit to millimetres, centimetres, metres or inches, and choose the output area unit from mm², cm², m² or in². The results bar returns the aperture area, diameter, radius and circumference, while the detail panels below show the area converted into all four units at once and a full worked calculation using A = π × r², so you can see every step from radius squared through to the final area. This is useful for photographers comparing how much light different f-stops let through, astronomers sizing telescope mirrors, or anyone needing the area of a round opening for design or DIY work. Because light-gathering power scales with area rather than diameter, small changes in aperture diameter make a big difference to the result, so it pays to check your units carefully before comparing figures.
1. Input Method
2. Unit Conversion
All Area Units
Worked Calculation
What is Aperture Area?
An aperture is any opening through which light (or other radiation) passes. In optics, the aperture of a lens or mirror is the effective circular opening that admits light. The aperture area determines how much light the system collects, because light collection scales with the cross-sectional area of the opening, not just its diameter.
Since most apertures are circular, the area formula is simply the area of a circle: A = π × r², where r is the radius. You can also express this as A = π × (D/2)² when you know the diameter D.
The Aperture Area Formula
For a circular aperture with diameter D and radius r = D/2:
- A = π × r²
- A = π × (D/2)² = (π / 4) × D²
For a 50 mm diameter aperture: r = 25 mm, A = π × 625 = 1,963.50 mm² (approximately 19.635 cm²).
Optics: f-Number and Effective Aperture
In photography and astronomy, the aperture is often described using the f-number (f-stop). The f-number is the ratio of the focal length to the effective aperture diameter:
- f-number = focal length ÷ aperture diameter
- aperture diameter = focal length ÷ f-number
For example, a 200 mm focal length lens set to f/4 has an effective aperture diameter of 200 ÷ 4 = 50 mm and an area of approximately 1,963.50 mm². Changing to f/5.6 (which increases the f-number by √2) halves the aperture area to approximately 981.75 mm², halving the light collected and requiring twice the exposure time.
Reference Table: Aperture Diameter and Area
| Diameter (mm) | Radius (mm) | Area (mm²) | Area (cm²) |
|---|---|---|---|
| 10 | 5 | 78.54 | 0.785 |
| 25 | 12.5 | 490.87 | 4.909 |
| 50 | 25 | 1,963.50 | 19.635 |
| 100 | 50 | 7,853.98 | 78.540 |
| 150 | 75 | 17,671.46 | 176.715 |
| 200 | 100 | 31,415.93 | 314.159 |
| 300 | 150 | 70,685.83 | 706.858 |
Why Aperture Area Matters
Light-gathering power is proportional to aperture area. Doubling the diameter quadruples the area and therefore quadruples the amount of light collected. This is why astronomers prize large telescope mirrors: a 300 mm mirror collects about 36 times more light than a 50 mm aperture (since (300/50)² = 36). In practical photography, each full stop (e.g., f/4 to f/5.6) halves the aperture area and therefore halves the exposure, requiring a shutter speed twice as long or an ISO twice as high to achieve the same brightness.
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Sources and method: Area of a circle: A = πr² (standard Euclidean geometry). Optics f-number definition: ISO 517:2022 Photography and optics. Aperture diameter from f-number: D = f / N, where f is focal length and N is f-number.
This calculator computes the geometric area of a circular aperture. For real optical systems, the effective collecting area may be reduced by obstruction (e.g., secondary mirrors in reflecting telescopes) or vignetting. Results are for a clear, unobstructed circular opening.