Mirror Equation Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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A mirror equation result can look precise while still being wrong if one unit or convention is off. Optical calculations are unforgiving of unit and sign mistakes because wavelength, angle, focal length, and refractive index can change a result quickly. This page keeps the calculation focused so the number is easy to trace back to the values you entered.

What this calculator does

The purpose of the Mirror Equation Calculator is to evaluate image distance from Mirror type, Object distance (−), Focal length (−). It is most useful for quick comparisons or hand-checks where the input definitions and displayed units remain part of the answer.

How to use it

Fill in the active quantities—Object distance (−), Focal length (−)—and leave output-only boxes for the calculator to derive. Choose Mirror type so the calculation path matches your case. Pay special attention to signs, angles, and whether a dimension is a radius, diameter, area, or length. Read the result together with its displayed unit.

How the calculation works

For curved mirrors, the page solves 1/f = 1/u + 1/v using its signed object, image, and focal-distance convention. Radius of curvature is r = 2f, linear magnification is −v/u, and areal magnification is the square of the linear value. Plane-mirror mode sets v = −u.

Example

Using the default example on the page (Mirror type = Concave mirror; Object distance (−) = -6 m; Focal length (−) = -12 m), the calculator returns image distance of 12 m. A modest change to one driving input should move the answer in the direction predicted by the equation, which is a useful unit check.

How to interpret the result

Read the image distance as the optical quantity defined by this page, not as a general rating of image or beam quality. Keep the displayed unit attached, and compare cases only after checking that angles, distances, wavelengths, and refractive indices use the same convention.

Limitations and notes

Mirror calculations are sensitive to sign convention. This page uses its own signed object/focal/image labels, so do not mix values copied from a textbook that uses the opposite convention. Spherical aberration and off-axis rays are outside the paraxial model.