Mirror Equation Calculator

1/f = 1/d_o + 1/d_i. Same form as lens but with mirror sign conventions.

Inputs

Result

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General calculation reads

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How Not to Be Wrong
Jordan Ellenberg - math thinking
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The Joy of X
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Scientific calculator (Casio fx-991EX)
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How to use this calculator

  • Pick what to solve.
  • Enter known values.
  • Mind sign conventions for concave/convex.

About this calculator

Mirror equation: 1/f = 1/d_o + 1/d_i. Sign convention: concave (converging) f positive; convex (diverging) f negative. Real images form on the reflective side (d_i positive); virtual images appear behind the mirror (d_i negative). Concave mirrors: bathroom shaving, dental, telescope primaries. Convex mirrors: passenger side car (objects appear smaller but wider field of view).

Frequently asked

Concave vs. convex?+
Concave: curves inward (like a spoon's bowl side). Convex: curves outward.
Why "objects in mirror are closer"?+
Convex mirror produces virtual diminished image. Brain reads diminished as far away — but it's actually closer than perceived.
Magnification > 1?+
Yes for concave when d_o < |f|. The classic shaving mirror — close = larger upright.
Plane mirror?+
f → ∞. d_i = -d_o (virtual, behind by same distance). M = 1 (same size, upright, reversed).
Telescopes?+
Newtonian: concave primary mirror at one end, secondary deflects to eyepiece. Big aperture = lots of light.

Related calculators

Thin Lens Equation Calculator
1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.
Focal Length from Radius (f = R/2)
For spherical mirror: f = R/2. For thin lens: 1/f = (n−1)(1/R₁ − 1/R₂) (lensmaker).
Magnification Calculator
M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.
Snell's Law Calculator
n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.
Wavelength ↔ Frequency Calculator
c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.
Centripetal Force Calculator
F_c = m × v² / r. Force required to keep object in circular motion.

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1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.

Focal Length from Radius (f = R/2)
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For spherical mirror: f = R/2. For thin lens: 1/f = (n−1)(1/R₁ − 1/R₂) (lensmaker).

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M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.

Centripetal Force Calculator
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F_c = m × v² / r. Force required to keep object in circular motion.

Snell's Law Calculator
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n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.

Fill PDF Form
PDF

Pre-fill a fillable PDF form (AcroForm) — type one line per field as `name=value`. Output is a filled PDF you can sign or print.