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Physics Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Lens Calculator

You can solve the thin-lens equation for focal length, object distance or image distance, and see the magnification, real or virtual image type and the sign convention used.

Runs in your browserFree · No sign-up · No watermark
lens → f, dᵢ, mRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
lens → f, dᵢ, m
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Physics Tools

About Lens Calculator

The thin-lens equation connects where an object sits, where its image forms and the lens's focal length: 1/f = 1/dₒ + 1/dᵢ. The magnification m = −dᵢ/dₒ tells you whether that image is enlarged or reduced, while the signs reveal whether it is real or virtual and inverted or upright.

This calculator solves for whichever quantity you are missing, in centimeters or meters, and explains the result in plain language. It also states the sign convention explicitly, because a negative image distance or magnification is information rather than an error, and warns when no real image can form.

What this tool does

The details that matter when you use Lens Calculator for real work.

  • Solve all three lens quantities

    Calculate focal length from the two distances, object distance from focal length and image distance, or image distance from focal length and object distance.

  • Magnification and orientation

    The magnification m = −dᵢ/dₒ is reported with inverted or upright and enlarged or reduced labels.

  • Real or virtual image

    The image type and the side it forms on are explained, with a note that virtual images cannot be projected on a screen.

  • Sign convention stated

    Converging and diverging focal lengths and real and virtual image distances are defined on the page.

  • No-real-image warnings

    Objects inside the focal point and diverging lenses are flagged, because no real image forms in those cases.

  • Formula and substitution

    The thin-lens equation and magnification are printed with the values in meters, so the result can be checked.

How to use Lens Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Choose what to calculate

    Select focal length, object distance or image distance depending on the missing value.

  2. 02

    Enter the two known distances

    Type the values and choose centimeters or meters; the same unit applies to every length field.

  3. 03

    Watch the signs

    Use a positive focal length for a converging lens, and a negative image distance when the image is virtual.

  4. 04

    Read the image description

    The headline gives the solved distance, and the explanation gives magnification, orientation and whether the image is real or virtual.

  5. 05

    Check the working and warnings

    The formula panel shows the substitution in meters, and a warning appears when the arrangement cannot form a real image.

How this tool works

Works with
lens → f, dᵢ, m
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Uses the thin-lens and paraxial approximations; thick lenses, wide angles and aberrations are outside the model.
  • Applies to a single thin lens only; multi-element systems need ray tracing or lens-design software.
  • Assumes the same medium on both sides of the lens; a lens between different media needs a modified form of the equation.

Privacy and file handling

Distances and focal lengths are processed entirely in your browser. Nothing is uploaded, stored or logged, and no network request is made while you calculate.

Read the full privacy policy

Lens Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is the thin-lens equation?
It is 1/f = 1/dₒ + 1/dᵢ, where f is the focal length, dₒ is the object distance from the lens and dᵢ is the image distance. The equation assumes a thin lens and rays close to the optical axis, which is why it is called the paraxial approximation.
What does a negative image distance mean?
A negative dᵢ means the image is virtual and forms on the same side of the lens as the object, so it cannot be projected onto a screen. This happens with a magnifying glass when the object is inside the focal point, and with diverging lenses.
What does a negative magnification mean?
A negative m means the image is inverted relative to the object, which is what a single converging lens produces when the object is beyond the focal point. The absolute value of m gives the size ratio: |m| above 1 is enlarged and below 1 is reduced.
How do I know whether a lens is converging or diverging?
Use the sign of the focal length: positive for a converging lens, which is thicker in the middle, and negative for a diverging lens, which is thinner in the middle. The calculator takes the sign you enter and reports when the resulting image must be virtual.
Why is no image formed when the object sits exactly at the focal point?
Rays from that point leave the lens parallel to each other, so they never converge and the image distance tends to infinity. The calculator reports this case as an error instead of showing a huge number, because no finite screen position would show a sharp image.
Does this calculator work for mirrors as well?
No. Mirrors have analogous equations, but their sign conventions and focal-length definitions differ from thin lenses. Use a dedicated mirror calculator rather than changing the signs here, so the real and virtual image interpretation stays correct.
Why is the image from a single converging lens upside down?
Rays from the top of the object cross the axis at the lens and arrive at the bottom of the image, so a real image formed beyond the focal point is inverted. The magnification m = −dᵢ/dₒ carries that sign, with m negative for an inverted image.
How accurate is the thin-lens model?
It is accurate for thin lenses and rays near the optical axis, which covers most introductory problems and simple magnifiers. Thick lenses, large apertures and wide angles introduce spherical and chromatic aberrations that the model does not capture, so real designs need ray tracing or lens software.

Background reading

Format guides that explain the trade-offs behind Lens Calculator.