Lens Equation Calculator

How to use the Lens Equation Calculator

1. 1Enter the focal length and the object distance, or the object and image distances.
2. 2Pick the units or options from the menus if the image distance tool offers them.
3. 3Read the image distance in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the image distance

Students use the equation for optics homework, photographers to understand focusing and enlarging, and hobbyists to build telescopes, projectors and magnifiers. The sign of the result tells you where to put a screen or whether you need to look through the lens.

A real image can be caught on a screen; a virtual image cannot, but you can see it by looking through the lens. A diverging lens always gives a smaller, upright, virtual image of a real object.

How the image distance is worked out

1 ÷ f = 1 ÷ object distance + 1 ÷ image distance. Magnification = −image distance ÷ object distance. A positive focal length is a converging lens; a negative one is diverging. A converging lens with f = 10 cm and an object 30 cm away forms a real image 15 cm behind the lens, half the size and upside down (magnification −0.5). With the object at 5 cm, inside the focal length, the image is virtual, 10 cm on the same side, upright and twice the size: a magnifying glass.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Image and focal length modes
• Real or virtual, upright or inverted
• Lens power in dioptres

Mistakes to avoid with image distance

Use the same unit for every length. The equation works for thin lenses and for rays close to the axis. Thick lenses and wide beams have aberrations that the formula ignores. If the object is exactly at the focal point, the image is at infinity and no finite answer exists.

On phone and computer

On a phone, type into the boxes one after another and read the image distance underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the image distance move. The lens equation calculator works the same on both. Lens maths pairs well with other light calculations. Check bending at a surface with the Snell's Law Calculator, find the wavelength of light with the Wavelength Calculator, and use the Trigonometry Calculator for angles.

Features

• Same unit everywhere
• Positive f converges
• Object at f gives no image
• Clear messages when the image distance inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions