Field of View Calculator

What is this?

A Field of View (FOV) Calculator works out how much of a scene an optical system can see. For a camera it gives the angle of view a lens produces on a given sensor and the width covered at a set distance; for a telescope it gives the patch of sky an eyepiece or camera shows, along with magnification, exit pupil, focal ratio and resolving power.

How to Use the Field of View Calculator

A Field of View (FOV) Calculator works out how much of a scene an optical system can see. For a camera that means the angle of view a lens gives on a particular sensor, and how wide a scene it covers at a given distance. For a telescope it means the patch of sky an eyepiece or camera shows, along with magnification, exit pupil and resolving power.

All three modes come down to the same relation between a sensor and a focal length, so a short lens on a big sensor and a short telescope with a big camera behave the same way.

1. Choose Your Setup

Pick one of the three tabs: Camera lens for photography, Telescope + eyepiece for visual observing, or Telescope + camera for astrophotography.

2. Enter the Optics

For a camera, select a sensor format - which fills the sensor dimensions - and enter the lens focal length. For a telescope, enter its focal length and aperture in millimetres and choose a Barlow or focal reducer if you use one.

3. Add the Eyepiece or Sensor

In visual mode enter the eyepiece focal length and its apparent field of view, both printed on the eyepiece. In imaging mode enter the camera resolution in pixels, the pixel size in micrometres and any binning.

4. Set a Distance (Camera Mode)

Optionally enter how far away your subject is. The calculator then reports the width and height of the scene covered at that range, not just the angle.

5. Read the Results

You get the field of view plus the supporting figures - crop factor and equivalent focal length for cameras, or magnification, exit pupil, focal ratio and Dawes limit for telescopes, along with the full working.

Key Formulas Used in the Calculator

Angle of View

$\text{AOV} = 2\arctan\left( \frac{\text{Sensor Size}} {2 \times \text{Focal Length}} \right)$

Applied separately to the sensor's width, height and diagonal to give the horizontal, vertical and diagonal angles of view. This exact form holds at any focal length, unlike the small-angle approximation, which drifts by several percent on wide fields.

Linear Field of View

$\text{FOV} = 2\tan\left( \frac{\text{AOV}}{2} \right) \times \text{Distance}$

Converts the angle into the actual width covered at a given distance. Because it is linear in distance, doubling the distance doubles the width covered.

Telescope Magnification and True Field

$\text{Magnification} = \frac{\text{Telescope Focal Length}} {\text{Eyepiece Focal Length}}$

$\text{True FOV} = \frac{\text{Apparent FOV}} {\text{Magnification}}$

A 1000 mm telescope with a 25 mm eyepiece gives 40x. If that eyepiece has a 52 degree apparent field, the true field of view is 52 ÷ 40 = 1.3 degrees.

Exit Pupil and Dawes Limit

$\text{Exit Pupil} = \frac{\text{Aperture}} {\text{Magnification}}$

$\text{Dawes Limit} = \frac{116} {\text{Aperture (mm)}}$

The exit pupil is the width of the light cone leaving the eyepiece; above about 7 mm some light misses a dark-adapted eye. The Dawes limit is the finest detail the aperture can resolve, in arcseconds.

Benefits

• Covers camera lenses, telescope eyepieces and astrophotography in one tool

• Uses the exact arctangent formula rather than the small-angle shortcut

• Ten sensor presets from medium format down to 1/2.3 inch

• Reports crop factor and 35 mm equivalent focal length

• Gives exit pupil, focal ratio and Dawes limit for telescopes

• Applies a Barlow or focal reducer to the focal length correctly

• Warns when a setup is over or under sampled, or the exit pupil is too wide

When & Where to Use

• Choosing a lens that will fit a subject in frame at a known distance

• Comparing the same lens on a full-frame and a crop-sensor body

• Checking whether a galaxy or nebula fits your telescope's field

• Picking an eyepiece for wide-field or high-magnification viewing

• Matching a camera to a telescope for the right image scale

• Working out whether a Barlow or reducer gets you the framing you want

• Planning security-camera or surveying coverage at a set range

Who Should Use This Calculator

The Field of View Calculator is useful for photographers, videographers, amateur astronomers, astrophotographers, drone and security-camera operators, and anyone choosing between lenses, eyepieces or sensors.

Tips to Get the Best Deal

Sensor size matters as much as focal length - the same lens is wider on a bigger sensor

Crop factor compares any sensor to full frame using the diagonal

A Barlow multiplies focal length; a reducer divides it, and both change the focal ratio

Aim for roughly 1 to 2 arcseconds per pixel for typical seeing

Keep the exit pupil under about 7 mm or you waste the aperture you paid for

Binning changes the arcseconds per pixel but never the field of view

Quoted focal lengths are nominal; real lenses vary slightly, especially when focused close

Pro Tips

• Sensor size matters as much as focal length - the same lens is wider on a larger sensor.

• Crop factor compares a sensor's diagonal to full frame's 43.27 mm.

• A Barlow raises magnification and narrows the field; a reducer does the opposite.

• Aim for about 1 to 2 arcseconds per pixel in astrophotography.

• Keep the exit pupil below roughly 7 mm so no gathered light is wasted.

• Binning changes arcseconds per pixel but never the field of view.