Calculate the focal length of a lens using the thin lens equation. Enter the object distance and image distance to get the focal length, along with magnification and angle of view. You can also work backwards — enter a known magnification and object distance to find the focal length directly.
Focal Length
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Magnification
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Angle of View
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Image Size
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Focal length is the distance between the rear principal point of a lens and the image sensor (or focal point) when the lens is focused at infinity. It is typically measured in millimeters (mm) and determines how much of a scene the lens captures — shorter focal lengths give a wider field of view, while longer focal lengths give a narrower, more magnified view.
The thin lens equation is: 1/f = 1/i + 1/o, where f is the focal length, i is the image distance, and o is the object distance. Rearranging gives: f = (o × i) / (o + i). All values must be in the same unit (usually millimeters).
If you know the magnification (M) and object distance (o), use: f = o / (1 + 1/|M|). For example, with magnification 0.00553× at an object distance of 10,000 mm (10 m), the focal length would be approximately 55.0 mm.
Magnification (M) is defined as the ratio of image size to object size, and equals the negative of image distance divided by object distance: M = −i/o. A magnification less than 1 means the image is smaller than the object, and greater than 1 means the image is larger. Longer focal lengths produce greater magnification for a given object distance.
The angle of view describes how much of a scene a lens captures, measured in degrees. It depends on both the focal length and the sensor size. A shorter focal length produces a wider angle of view, while a longer focal length produces a narrower angle. The formula is: AOV = 2 × atan(sensor_size / (2 × f × (|M| + 1))) × (180/π).
Object distance (o) is the distance from the lens to the subject being photographed. Image distance (i) is the distance from the lens to the image plane — typically where the camera sensor or film sits. Both distances together determine the focal length through the thin lens equation.
Yes, in general a longer focal length means a narrower field of view and higher magnification, which gives a zoom effect. However, the apparent zoom also depends on your sensor size — the same physical lens will appear more zoomed on a smaller (crop) sensor than on a full-frame sensor, due to the crop factor.
All distance inputs (object distance, image distance, and sensor size) should be in the same unit — this calculator uses millimeters (mm). If your distances are in meters or centimeters, convert them to millimeters first (1 m = 1000 mm, 1 cm = 10 mm).