Focal Length to Angle of View Calculator
Convert a focal length into its angle of view, or work backwards from the angle you need to the lens that covers it.
Results
- Horizontal angle of view
- 54.4°
- Vertical angle of view
- 37.8°
- Diagonal angle of view
- 63.4°
- Full-frame equivalent focal length
- 35mm
How wide a slice of the scene the frame captures, left to right.
How tall a slice of the scene the frame captures, top to bottom.
Corner to corner. This is the figure lens manufacturers usually print on the box, which is why it always sounds wider than the view feels.
A full-frame camera would need this focal length to frame the same view, based on this sensor's 1.00× crop factor.
How it works
Focal length is a property of the lens, but angle of view is what you actually see. The link between them runs through the sensor: the same lens covers a wider angle on a larger sensor, which is the whole reason crop factors exist.
Working forwards tells you what a lens will give you. Working backwards is more useful when planning: if you know you need to cover 90 degrees to fit an interior, or 8 degrees to frame the moon, this tells you the focal length that gets there before you rent or buy anything.
Because the relationship runs through a tangent rather than a straight line, it is strongly non-linear. Going from 200mm to 100mm roughly doubles the angle, but going from 20mm to 10mm nearly doubles it again in a range where every millimetre counts. This is why wide-angle lenses are sold in such small increments.
The formula
angle = 2 × arctan(d / 2f), f = d / (2 × tan(angle / 2))
d is the sensor dimension the angle is measured across: width for horizontal, height for vertical, or the diagonal. No rectilinear lens can reach 180 degrees, since the focal length would have to fall to zero.
Frequently asked questions
- What focal length matches human vision?
- There is no single answer, because the eye's sharp central vision is narrow while its total field is enormous. The usual convention is that a lens matching the sensor diagonal, about 43mm on full frame, gives perspective that looks natural, which is why 35mm and 50mm both feel normal.
- Why can't I get 180 degrees?
- In a rectilinear lens, one that keeps straight lines straight, reaching 180 degrees would require a focal length of zero. Fisheye lenses reach and exceed it by abandoning rectilinear projection and bending straight lines instead.
- Should I enter my lens's equivalent focal length?
- No, enter the real focal length printed on the barrel and pick your sensor format. The calculator applies the crop factor itself and shows the full-frame equivalent as a result.
- The required focal length isn't a lens that exists. What now?
- Round down to the nearest lens you can get. A slightly shorter focal length covers a slightly wider angle, so you keep everything you needed in frame and can crop in afterwards. Rounding up risks cutting off the edges.