Lens Magnification Calculator
Where a lens forms an image and how large it is — with whether the image is real or virtual, upright or inverted.
The thin-lens equation is 1/f = 1/u + 1/v, and magnification is −v/u.
How the lens magnification calculator works
The thin-lens equation is 1/f = 1/u + 1/v, and magnification is −v/u. The signs carry the physics: a negative image distance means the image is virtual and on the same side as the object, and a negative magnification means it is inverted.
That is why a magnifying glass held close gives an upright enlarged image and held far away gives an inverted one — the object crosses the focal point and the sign flips.
Formula: 1/f = 1/u + 1/v; m = −v/u
Worked examples
| Inputs | Magnification | Note |
|---|---|---|
| Object beyond the focal point | -2 | real, inverted, 2× enlarged |
| Object inside it | 2 | virtual and upright — a magnifying glass |
| A diverging lens | 0.4 | always virtual and reduced |
FAQFrequently 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. It assumes the lens is thin compared with the distances.
What does a negative magnification mean?
The image is inverted. The sign is physics, not an error.
What is the difference between a real and a virtual image?
A real image can be caught on a screen because light actually converges there. A virtual image cannot — the light only appears to come from it.
Why does a magnifying glass sometimes show things upside down?
Because you moved past the focal point. Inside it the image is upright and virtual; beyond it, inverted and real.
What is lens power?
The reciprocal of the focal length in metres, in dioptres. A 10 cm lens is 10 dioptres, which is how spectacle prescriptions are written.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.