Thin Lens Calculator
Find focal length from object and image distance.
Distance from lens to object.
Distance from lens to image.
Results update as you type.
How it works
The thin lens equation is the cornerstone of geometric optics, linking a lens's focal length to where an object sits and where its image forms. This thin lens calculator takes the object distance and image distance you measure and returns the focal length in centimetres. The focal length describes how strongly a lens bends light: a short focal length bends rays sharply, while a long one bends them gently, and it stays fixed for a given lens regardless of what you view through it. This matters throughout photography, vision science, and instrument design. It determines where a camera must focus, how eyeglasses correct blurry vision, and how microscopes and telescopes magnify. By relating three measurable distances, the equation lets you predict image position, design lens systems, and diagnose focusing problems. A thin lens calculator removes the fiddly reciprocal arithmetic, so you can move quickly from measured distances to the focal length that characterises the lens. The formula works because a thin lens bends incoming light by a fixed amount, so rays from an object at a given distance always converge to a predictable image distance. Adding the reciprocals of those two distances yields the reciprocal of the focal length. Following the sign convention, where real images and converging lenses take positive values, students, photographers, and optical engineers rely on a thin lens calculator to design and understand imaging systems.
1/f = 1/dₒ + 1/dᵢ
The thin lens equation relates the focal length of a lens to the distances of the object and its image because a lens bends light by a fixed amount set by its shape, focusing rays from a given object distance to a matching image distance. Adding the reciprocals of the object and image distances gives the reciprocal of the focal length, so the focal length is one divided by that sum. The formula works for lenses thin enough that their thickness is negligible, letting all the bending be treated as happening at a single plane, which keeps the geometry of converging rays simple.
Source:Standard physics (thin lens equation)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter object distance and image distance.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Focal length updates instantly as you type — no button to press.
Frequently asked questions
What sign convention does this calculator use?
This calculator follows the common convention where distances measured on the real side of the lens are positive. For a converging lens forming a real image, both the object distance and image distance are positive, giving a positive focal length. If you are working with virtual images or diverging lenses, enter the appropriate negative distances, and the resulting focal length sign will correctly indicate whether the lens converges or diverges light.
What does the focal length tell me about a lens?
Focal length measures how strongly a lens converges or diverges light. A short focal length bends rays sharply and produces a wide field of view with strong magnification changes, while a long focal length bends light gently and narrows the field. In cameras, short focal lengths give wide-angle shots and long ones give telephoto zoom. The focal length is a fixed property of the lens set by its shape and material.
What is the difference between a real and virtual image?
A real image forms where light rays actually converge and can be projected onto a screen, like the image inside a camera or on a cinema screen. A virtual image forms where rays only appear to originate, such as the upright, magnified view through a magnifying glass, and cannot be projected. The sign of the image distance tells you which type you have: positive for real, negative for virtual, in this convention.
Why is it called the thin lens equation?
The equation assumes the lens is thin enough that its physical thickness is negligible compared with the object and image distances. This lets all the light bending be treated as if it happens at a single plane in the centre of the lens, which greatly simplifies the geometry. Real thick lenses require more complex modelling with principal planes, but for most everyday lenses the thin lens approximation is accurate and convenient.
Can I use this equation to find magnification?
Yes, once you know the object and image distances you can find magnification separately as the negative ratio of image distance to object distance. A magnification magnitude greater than one means the image is enlarged, while less than one means it is reduced, and a negative sign indicates the image is inverted. This calculator focuses on focal length, but the same two distances feed directly into that magnification relationship.