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Thin Lens Focal Length and Field Angle

The paraxial thin-lens model uses magnification equal to image size divided by object size, and focal length equal to object distance times magnification divided by one plus magnification.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Worked example: magnification = 0.01; focal length = 99.00990099009900990099009900990099009900990099009900990099009900990099009900990099009900990099009901; angle of view2 = 5.724810452223495065386689456967666704662825811025401602238554282206790732925493049851024422848835201. See the assumptions for units and model limits.

magnification = image_size / object_size; focal_length = (object_distance / (( 1 / magnification ) + 1 ))*1000; angle_of_view2 = (180/pi) * 2 * atan (image_size / ( 2 * focal_length * ( magnification + 1 )))

Worked example

Enter these known values and leave the other values blank.

Object size
100 cm
Image size
10 mm
Object distance
10 m
Magnification
0.01 ×
Focal length
99 mm
Angle of view
5.725 deg

Assumptions and limitations

  • The paraxial thin-lens model uses magnification equal to image size divided by object size, and focal length equal to object distance times magnification divided by one plus magnification.
  • Field angle uses the finite-conjugate effective image distance f times one plus magnification. Sizes are positive magnitudes, excluding signed virtual-image conventions, lens distortion and focus breathing.

Common questions

What does this model assume?

The paraxial thin-lens model uses magnification equal to image size divided by object size, and focal length equal to object distance times magnification divided by one plus magnification.

Can I solve for a different value?

Clear the desired editable unknown and enter sufficient independent known values. Unit selectors preserve quantities; singular or unsupported inverse branches remain incomplete.

References

Reject singular physical denominators and fractional discrete counts using exact isInteger checks.

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