Focal Length Calculator - Lens, Magnification, and Angle of View

A focal length calculator applies the thin lens equation 1/f = 1/o + 1/i, magnification m = -i/o, and the chosen sensor diagonal to return the four numbers a photographer needs before pressing the shutter: focal length, image distance, magnification, and angle of view. Pick a sensor from compact 1/4 inch to 35mm full frame, choose millimeters or meters, then enter any two of focal length, object distance, or image distance and the page returns the third plus the angle of view.

• • Find The Right Lens For A Subject Distance: Type the working distance and sensor diagonal, then read the focal length that frames the shot.
• • Convert A Magnification Spec To Focal Length: Enter object distance and the magnification your macro setup needs, and read the matching focal length.
• • Compare Angle Of View Across Sensor Formats: Switch between 1 inch type, APS-C, and 35mm full frame to see how the same focal length renders a tighter or wider scene.
• • Plan Macro And Close-Up Setups: Enter a real subject height and the sensor diagonal to derive magnification and confirm the lens extension.

The page applies three relationships: focal length satisfies 1/f = 1/o + 1/i; magnification equals image distance over object distance, also image size over object size; and the diagonal angle of view is 2 * atan(sensor diagonal / (2 * focal length)), converted to degrees.

Once the focal length, magnification, and angle of view are locked in here, Exposure Calculator converts the resulting aperture, shutter speed, and ISO into a single exposure value so the photographer matches the camera settings to the available light.

The calculator picks a sensor diagonal from the format table, applies the thin lens equation 1/f = 1/o + 1/i to the values you enter, and converts the resulting focal length into an angle of view. Give it any two of focal length, object distance, or image distance and it derives the third plus magnification and angle of view.

• focalLength: Lens focal length in millimeters, defined for a thin lens focused at infinity.
• objectDistance: Distance from the lens's front principal plane to the subject, in the chosen unit.
• imageDistance: Distance from the lens's rear principal plane to the sensor, in the chosen unit.
• magnification: Ratio of image size to object size, equivalent to image distance over object distance for a thin lens.
• sensorDiagonal: Diagonal of the camera sensor or film frame in millimeters, picked from the format table.
• angleOfView: Diagonal angle of view in degrees, computed from sensorDiagonal and the effective focal length.

Switching between millimeters and meters scales object and image distance by 1000 before re-running the equations, so a 10 m subject reads like a 10000 mm subject.

According to HyperPhysics - Thin Lens Equation, thin lens equation 1/f = 1/o + 1/i and sign conventions for converging lenses

When the same focal length has to span many frames of motion picture film instead of a single still, Film Calculator plans the run-time, fps, and roll count using the same lens-side information you set here.

Four ideas drive every focal length, magnification, and angle of view the calculator returns.

Magnification and sensor size feed each other. Doubling the diagonal at the same focal length doubles the angle of view; doubling the focal length at the same sensor halves it.

A drone carrying the camera body you sized here has to hover long enough to nail the framing, so Drone Flight Time Calculator plans the flight time so the focal length and angle of view you locked in get captured in the air.

Walk through the inputs in order and the result updates as you type.

1. 1 Pick A Sensor Format: Open the Sensor Format menu and choose your camera body. The diagonal updates the Angle of View readback.
2. 2 Choose A Distance Unit: Pick millimeters for lens-style precision or meters for friendly subject distances. The Object and Image Distance fields rescale.
3. 3 Enter Any Two Optical Distances: Type focal length, object distance, or image distance - whichever two you know. Leave the third at zero to solve.
4. 4 Add Object Size For Magnification: Fill in Object Size to confirm magnification from subject height, or leave it blank to derive magnification from distances.
5. 5 Read Focal Length And Angle Of View: Watch focal length, image distance, magnification, and angle of view update. Compare the angle against the chosen body.
6. 6 Compare Across Sensor Formats: Switch between 1 inch, APS-C, and Full Frame to see how the same focal length renders a different angle of view.

Framing a 1.8 m subject on a full-frame body for a tight portrait: set Sensor Format to Full Frame (35mm), Distance Unit to mm, type 10000 mm into Object Distance and 55.3 mm into Image Distance, and leave Focal Length at 0. The page returns 55 mm focal length, 0.00553x magnification, and a 43.0 degree diagonal angle of view.

When the still camera moves into a time-lapse rig and the focal length has to stay sharp across hundreds of frames, Time Lapse Calculator plans the interval and total clip length using the same sensor and lens setup you configured here.

Putting the thin lens equation, magnification, and angle of view into one tool saves setup time and mismatched gear on every shoot.

• • Match Lens To Subject Distance: Type the working distance and sensor diagonal, then read the focal length that frames the shot.
• • Pick A Sensor Body With Confidence: Compare APS-C, full frame, and 1 inch sensors side by side to see which body delivers the field of view your lens lists.
• • Translate Macro Specs Into Focal Length: Enter the magnification your close-up setup needs and read the focal length that lands the subject on the sensor.
• • Plan Multicopter And Drone Payloads: Use object distance and sensor diagonal to size a lens for an aerial survey, then convert the result into a flight plan and battery budget.
• • Keep Diagonal And Horizontal Angles Aligned: Read both angles of view so framing math stays consistent between the viewfinder preview and the final still.

Used consistently, the page is a planning document as much as a calculator, keeping the cinematographer and photographer on the same focal length story.

Long focal-length shoots on a tripod drain the camera, monitor, and follow-focus faster than quick photo sessions, so Battery Size Calculator sizes the battery pack for the lens and sensor combination you locked in here.

Four practical factors decide how close the calculator stays to the framing you see in the viewfinder.

• • The page assumes a thin lens and the paraxial approximation. Real lenses add elements that can shift the effective focal length by a few percent at close focus.
• • Sensor diagonals are nominal CIPA measurements and actual sizes vary slightly between vendors. Treat the angle of view as a planning figure within roughly 2 percent.
• • Magnification at the sensor diagonal is an approximation. Real shots usually match the longer sensor edge to subject height, so framing shifts a touch from the readback.

Treat the result as the centre of a planning envelope. Round the focal length to the nearest standard prime and confirm with a test shot.

According to CIPA Standard Image Sensor Format Sizes, standard image sensor format diagonal measurements for compact and interchangeable-lens cameras

Once the focal length, sensor diagonal, and angle of view feed a 3D scene render that mimics the camera body, 3D Render Time Calculator translates the frame total and ray count into a render time estimate.