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Thin Lens Equation Calculator

Solve for image distance and lateral magnification using the real-is-positive sign convention for an ideal thin lens. A negative focal length represents a diverging lens.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Image distance (cm)15
Lateral magnification-0.5

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

Thin-lens equation 1/f = 1/dₒ + 1/dᵢ; lateral magnification m = −dᵢ/dₒ.

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Focal length (cm) = 10, Object distance (cm) = 30, the formula returns Image distance (cm) = 15, Lateral magnification = -0.5. The displayed default result is generated from these same inputs.

Limitations and safety

Assumes a thin paraxial lens in one medium. Thick-lens effects, aberrations, wavelength dependence and multi-element systems are excluded. Never look at the Sun through a lens. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

What does negative magnification mean?

It indicates an inverted image under this sign convention; the absolute value is the size ratio.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

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