Focal Length Calculator

Understanding Focal Length

Focal length is the distance from the lens optical center to the sensor where light converges. It controls field of view and magnification. A 50 mm lens on full frame is a classic normal view, while 200 mm compresses perspective for distant subjects.

Focal Length Formulas

From object distance and magnification:

$$f = \frac{d_o}{(1/m) + 1} \times 1000$$

Thin lens equation with distances in millimeters:

$$\frac{1}{f} = \frac{1}{d_i} + \frac{1}{d_o}$$

Angle of view from sensor size:

$$\theta = \frac{180}{\pi} \times 2 \times \arctan\left(\frac{\text{sensor width}}{2 f (m + 1)}\right)$$

Frequently Asked Questions

What focal length matches 10 m at 0.00553x magnification?

About 55 mm. Small magnification values are normal when the subject is much larger than the sensor image.

How does sensor size affect angle of view?

A wider sensor sees more of the scene at the same focal length. That is why crop factor converts lens focal lengths to full-frame equivalents.

What is the thin lens equation?

It relates object distance, image distance, and focal length for ideal lenses. Real lenses add distortion and aberrations, but the equation is a solid starting estimate.

Why is image distance negative?

Sign conventions mark real images on opposite sides of the lens from the object. Negative magnification indicates an inverted image.

Does focal length change when focused closer?

Internal focusing lenses adjust optical groups, so effective focal length can shift slightly at close distances. This calculator uses the stated nominal values.

What is a normal lens?

On full frame, roughly 43 mm matches human perspective. 50 mm lenses are the practical normal choice in most kits.

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Understanding Focal Length

Focal Length Formulas

Frequently Asked Questions

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