Lens Equation Calculator
Calculate image distance and magnification from focal length and object distance using the thin lens equation.
Last reviewed by the Radiatus Cloud team
Calculate image distance and magnification using the thin lens equation.
Need this done properly for your business?
Radiatus delivers secure cloud, DevOps & compliance engineering.
Use the thin lens equation
The thin lens equation relates the focal length of a lens to the distances of an object and its image: one over the focal length equals one over the object distance plus one over the image distance. This calculator solves for the image distance and the magnification, which is the negative ratio of the image distance to the object distance. It also interprets the result, telling you whether the image is real or virtual, upright or inverted, and enlarged or reduced. A convex lens has a positive focal length and a concave lens a negative one.
The sign conventions reveal a great deal: a positive image distance means a real image that can be projected on a screen, while a negative one means a virtual image.
Lenses and image formation
The thin lens equation is essential for understanding cameras, telescopes, microscopes, projectors and the human eye. Where an object sits relative to the focal point determines the nature and size of the image a lens forms, which is why moving a magnifying glass changes what you see. Magnification greater than one in absolute value means the image is larger than the object.
Use consistent units for all distances, and follow the sign convention of positive focal length for converging lenses. The calculator applies the standard convention and interprets the outcome. All calculation happens locally in your browser.
Related tools
- Security Term Translator — Translate complex security jargon into business language.
- Security Myth vs Reality — Fact-check common security myths.
- Breach News Impact — Contextualize major breaches into understandable analogies.
- Config Safety Analyzer — Paste a config snippet to check for obvious safety issues.
Frequently Asked Questions
What is the thin lens equation?
One over the focal length equals one over the object distance plus one over the image distance, relating the three for a thin lens.
What does a negative image distance mean?
It indicates a virtual image on the same side as the object, which appears upright and cannot be projected onto a screen.
What is magnification?
It is the negative ratio of image distance to object distance. Its sign shows orientation and its size shows whether the image is enlarged or reduced.
How do convex and concave lenses differ?
A convex, converging lens has a positive focal length, while a concave, diverging lens has a negative focal length.
Why does the image change as I move the object?
The image distance and magnification depend on where the object sits relative to the focal point, so moving it changes the image type and size.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the focal length and object distance.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.