Focal Length Calculator
Find the focal length needed to fill the frame with a subject of a given size.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
The thin lens relationship links subject size, image size and distance so that any three give the fourth. In practice this answers the common question of what lens is needed from the back of a room to frame a person or a stage.
Worked example
calculated with the default values below
Subject height 1.8 m · Distance to the subject 10 m · Sensor height Full frame (24 mm high) · How much of the frame to fill 90 % Focal length needed 118.6 mm · Magnification 0.0120 x · Angle of view 11.56 degrees · Image height on the sensor 21.60 mm · Field of view at this distance 2.02 m
General background references
Disclaimer
These calculators give general estimates. Sizing, pricing, availability and standards vary by brand, retailer and country, so treat the output as a starting point and confirm it against the seller's or authority's own figures.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
u = max(10, F) ÷ 100; f = D × 1000 × s × u ÷ (H × 1000 + s × u); α = 2 × atan(s ÷ (2f)) × 180 ÷ π
- H
- subject height (m)
- D
- shooting distance (m)
- s
- sensor dimension (mm)
- F
- frame fill (%)
- u
- fill fraction (10% floor)
- f
- focal length (mm)
- α
- angle of view (°)
u is the fill fraction with a 10% floor; magnification = s × u ÷ (H × 1000); field of view = D × s ÷ f.
Frequently asked questions
How does filling 90 percent of the frame change the lens?
The calculator treats 'fill' as the fraction of sensor height the subject occupies, so at 90 percent the projected image height equals sensor x 0.9. With a 24 mm sensor, a 1.8 m subject at 10 m then needs about 119 mm instead of the 132 mm a full-frame fill demands. Because focal length follows image height divided by subject height, a ten-point drop in fill cuts the lens requirement by roughly ten percent.