Method 1 — Object / image measurement
f = dodi / (do + di)
For a real image formed by a converging thin lens, use positive measured distances.
Focal length
–
mm
Optical power: – D
Lens Focal Length Calculator
Calculate the focal length of a thin lens using three complementary methods: measured object and image distances, Lensmaker's equation from surface radii and refractive index, or the Bessel method using a fixed object-screen distance. Optical power is also shown in diopters.
Method 2 — Lensmaker's equation
1/f = (n/nm−1)(1/R1−1/R2)
Use ∞ / inf for a plane surface. Light travels left → right; positive R has its center to the right.
Focal length
–
mm
Optical power: – D
Method 3 — Bessel method
f = (L2 − d2) / (4L)
Valid when L > d > 0 and two sharp-image positions exist.
Focal length
–
mm
Optical power: – D
Method 4 — Optical power
Φ = 1/f(m) = 1000/f(mm)
Positive power corresponds to a converging lens; negative power to a diverging lens.
Focal length
–
mm
Input optical power: – D
Comparison of results
Experimental power
–
DLensmaker power
–
DBessel power
–
DPower input → focal length
–
mm
Thin-lens model: the object/image method neglects lens thickness and principal-plane offsets; Lensmaker's equation is the thin-lens form and uses signed surface radii; the Bessel method assumes a fixed object-screen separation and two sharp-image positions. For thick lenses or high-precision optical design, the effective focal length and principal planes should be treated separately.
Calculation methods and sign convention
Object / image: 1/f = 1/do + 1/di.
Lensmaker in a surrounding medium: 1/f = (n/nm − 1)(1/R1 − 1/R2).
Bessel method: for fixed object-screen distance L and separation d between the two sharp-image lens positions, f = (L2 − d2)/(4L).
Optical power: Φ = 1/f(m) = 1000/f(mm).
Radius convention: light travels from left to right. R is positive when the center of curvature lies to the right of the surface and negative when it lies to the left.
Lens focal length calculation
This free online lens focal length calculator provides several standard ways to determine the focal length of a thin lens. The experimental object-image method uses measured object and image distances, while Lensmaker's equation relates focal length to refractive index and the radii of curvature of the two lens surfaces.
The Bessel method is useful in a laboratory setup when the distance between object and screen is fixed and the lens can be moved between two positions that produce sharp images. Comparing independent methods can be useful when checking an unknown lens or validating a measurement setup.
Typical applications
- Measure or verify the focal length of laboratory lenses.
- Estimate focal length from refractive index and surface curvature.
- Determine focal length with the Bessel displacement method.
- Convert optical power in diopters into focal length in millimeters.
Optical reference
Lensmaker's equation in this calculator is the thin-lens form. The refractive-index term is written relative to the surrounding medium, so the calculator can also be used when the lens is immersed in a liquid rather than surrounded by air.
For a plane surface, enter ∞, inf or infinity for the corresponding radius. Typical biconvex lenses use R1 > 0 and R2 < 0 under the stated left-to-right sign convention.
Lambda Physics also offers optical components, optical glass and coating materials in the General Stock catalog.