Mirror Radius of Curvature Calculator
A spherical mirror focuses light to a point at half its radius of curvature. Knowing the radius, you can find the focal length, and with an object distance you can find where the image forms and how large it is. This calculator uses the paraxial mirror relations: the focal length is half the radius, and the mirror equation links object distance, image distance, and focal length. Enter the radius of curvature and an object distance to get the focal length, image distance, and magnification.
Mirror equations
Focal length f = R / 2
1/do + 1/di = 1/f
Image distance di = (do * f) / (do - f)
Magnification m = -di / do
Use a positive radius for a concave mirror and a negative radius for a convex mirror. A positive image distance is a real image in front of the mirror; a negative value is a virtual image behind it. Negative magnification means an inverted image.
Spherical mirror facts
- The focal length of a spherical mirror is exactly half its radius of curvature.
- A concave mirror can form real, inverted images of distant objects.
- A convex mirror always forms an upright, reduced, virtual image.
- An object at the focal point produces no finite image (rays exit parallel).
- Wide-aperture mirrors show spherical aberration beyond the paraxial limit.
Mirror radius of curvature: frequently asked questions
How is the radius of curvature related to focal length?
For a spherical mirror, the focal length is half the radius of curvature: f = R / 2, so R = 2f. This holds for both concave and convex mirrors in the paraxial (small-angle) approximation, where rays stay close to the optical axis.
What is the mirror equation?
The mirror equation relates object distance, image distance, and focal length: 1 over object distance plus 1 over image distance equals 1 over focal length. Solving for the image distance gives di = (do times f) divided by (do minus f). This calculator returns the image distance for the object you enter.
How is magnification calculated?
Magnification equals minus the image distance divided by the object distance. A negative magnification means the image is inverted; a positive value means it is upright. The absolute value gives the size ratio between image and object.
What sign convention does this use?
This calculator uses positive focal length and radius for a concave mirror and positive object distance for a real object. A positive image distance means a real image in front of the mirror; a negative image distance means a virtual image behind it. Use a negative focal length for a convex mirror.
Does this assume small angles?
Yes. The relation f = R / 2 and the mirror equation are paraxial approximations valid for rays near the optical axis. Real mirrors with wide apertures show spherical aberration, where outer rays focus at a slightly different point than the paraxial focus.
Official sources
- NIST: Physical Measurement Laboratory: optics and geometric optics.
- NASA: NASA education resources on reflecting optics.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.