Magnification Calculator

Calculate optical magnification from object and image heights (m = hᵢ/hₒ) or distances (m = −dᵢ/dₒ). Includes angular magnification for simple magnifiers, telescopes, and microscope total magnification.

Lateral Magnification m
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Image Interpretation —
Extended More scenarios, charts & detailed breakdown ▾
Magnification m = hᵢ/hₒ
—
Interpretation —
Professional Full parameters & maximum detail ▾

Lateral Magnification

Lateral Magnification (heights) —
Lateral Magnification (distances) —

Advanced

Longitudinal Magnification m² —
Microscope Total Magnification —

How to Use This Calculator

  1. Select Calculate From: use Heights if you measured the object and image sizes; use Distances if you know the object/image distances.
  2. Enter the known values.
  3. Results show magnification and an interpretation (magnified/diminished, inverted/upright).
  4. Use Angular Magnification tab for simple magnifiers, telescopes, and microscopes.

Formula

Lateral: m = hᵢ/hₒ = −dᵢ/dₒ

Longitudinal: m_long = m²

Simple magnifier: M = 25/f + 1 (f in cm)

Telescope: M = f_obj / f_eye

Microscope: M_total = M_obj × M_eye

Example

Example: dₒ = 20 cm, dᵢ = −40 cm. m = −(−40)/20 = +2 (virtual, upright, 2× magnified). From heights: hₒ = 5 cm, hᵢ = 10 cm → m = 10/5 = +2.

Frequently Asked Questions

  • m = hᵢ/hₒ = −dᵢ/dₒ. A value of m = −2 means the image is twice as large and inverted. m = +0.5 means the image is half the size and upright. Negative m always indicates a real, inverted image.
  • Longitudinal magnification = m² (square of lateral magnification). This tells you how much an object's depth is stretched along the optical axis. Important for 3D objects imaged through a lens.
  • For a simple magnifier: M ≈ 25 cm / f (near-point formula) or M = 25/f + 1 (relaxed eye). For a telescope: M = f_objective / f_eyepiece. For a microscope: M_total = M_objective × M_eyepiece.
  • The sign convention m = −dᵢ/dₒ gives negative m when dᵢ > 0 (real image, opposite side of lens from object). Real images are always inverted relative to the object.
  • Optical magnification is the ratio of image size to object size (dimensionless). Photometric quantities like lumens/lux measure light intensity, not image geometry. They are completely separate concepts.

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Sources & References (5) ▾
  1. Magnification — HyperPhysics — Georgia State University
  2. OpenStax University Physics Vol 3, Ch 2.6 — The Eye — OpenStax
  3. Hecht, E. Optics (5th ed.) — Pearson
  4. Edmund Optics — Magnification Fundamentals — Edmund Optics
  5. MIT OCW 8.03 Vibrations and Waves — MIT OpenCourseWare