Lens Magnification Calculator - Solve m = h/g From f and d

A lens magnification calculator turns a converging lens's focal length and the total distance between the object and the sensor into a numeric magnification m = h/g, plus the object distance g and the image distance h that produce it. Enter f, d, and optionally an extension tube length, and the page returns magnification, object distance, image distance, effective image distance, and total magnification.

• • Pick the right telephoto for distant wildlife or sports: Type in 200 mm, 400 mm, or 600 mm and the distance to the subject to read the magnification before you frame the shot.
• • Plan a macro setup with extension tubes: Enter a 50 mm or 100 mm lens, the close working distance, and a tube length to read the magnification on the sensor.
• • Estimate subject size from a reference object: Use a known-size marker and the focal length to back-solve how big the subject looks relative to the sensor.
• • Compare prime lenses at the same focus distance: Run a 35 mm, 50 mm, and 85 mm prime to see how object distance and magnification move as the focal length grows.

Magnification in photography is almost always less than 1, because the image the lens projects onto a small sensor is much smaller than the subject itself, even with a long telephoto. This calculator works in the camera-lens sense: it computes the size ratio between the image on the sensor and the subject in front of the lens.

If you would rather solve for f, do, or di directly from the thin-lens equation 1/f = 1/do + 1/di, the Thin Lens Equation Calculator page uses the same formula and returns the same magnification as a free output.

The calculator combines two constraints, the thin-lens equation and the geometric focus-distance constraint, and solves them as a single quadratic in the object distance. The two roots fall out cleanly, and the magnification follows from their ratio.

• f: Focal length of the converging lens, in millimeters. Positive for a converging (real, convex) lens.
• d: Total focus distance between the object and the sensor, in the same unit as f, typically mm or m.
• g: Object distance from the object to the lens, in millimeters. The larger of the two roots.
• h: Image distance from the lens to the sensor, in millimeters. The smaller of the two roots.
• m: Linear magnification, m = h/g. Equals 1 when g equals h and approaches 0 as g grows much larger than h.
• e: Optional extension tube length, in millimeters. Adds to h, not to g, so it raises magnification without changing focus distance.

The two equations combine into a single quadratic because the geometry fixes g + h = d at the same time the thin-lens equation fixes 1/g + 1/h = 1/f. The discriminant has to be non-negative, which is why d must be at least 4 times the focal length.

According to Wikipedia, linear magnification of a thin lens is the ratio of the image height to the object height and, by similar triangles, equals the ratio of the image distance h to the object distance g, so m = h/g

When the focal length is not printed on the lens and you need to compute it from the refractive index and the surface radii of curvature, the Lensmakers Equation Calculator page is the right companion tool to run first.

Four short ideas show up every time you read or measure magnification, and each one feeds directly into the formula the calculator uses.

These four ideas appear together in any optics textbook chapter on real-image formation, but the focus-distance form d = g + h is the one you almost never see written out in introductory treatments.

If the focal length is negative (a diverging lens), the same equations do not give a real image on the sensor, so the calculator explicitly disallows that case. The same real-image quadratic governs curved mirrors, so the Mirror Equation Calculator page is a useful cross-check when you are studying how the lens derivation relates to its mirror analog.

Five quick steps turn a lens specification and a working distance into a magnification number, an object distance, and an image distance.

1. 1 Enter the focal length: Use millimeters. A 50 mm prime, a 200 mm telephoto, and a 100 mm macro all fit the same field, just at different numbers.
2. 2 Enter the focus distance: Type the distance between the subject and the sensor. For macro use mm, for wildlife and landscape use m.
3. 3 Pick the focus distance unit: Choose mm for working distance under a meter, m for telephoto setups. The page converts everything to mm internally.
4. 4 Add the extension tube length if you have one: If you are stacking a 12 mm, 25 mm, or 36 mm tube, enter its length in mm. Leave the field at 0 otherwise.
5. 5 Read the outputs: The page reports m = h/g as a unitless ratio, g and h in mm, and m' = (h + e)/g when a tube is present.

Suppose you own a 50 mm f/1.8 prime and want to know how big a 25 cm ruler will look at 500 mm subject-to-camera distance. Enter f = 50, d = 500, no tube. The page returns g = 443.65 mm, h = 56.35 mm, m = 0.127.

Once you know the magnification at each scheduled shot, the Time Lapse Calculator page helps you plan the shooting interval and clip length for a time-lapse sequence built around that framing.

Five concrete benefits show up when you pre-compute magnification instead of guessing it from the back of the camera.

• • Predict the frame size before you shoot: Read the magnification before the shoot, then multiply by the sensor width to know how many millimeters of subject will land on the chip.
• • Compare focal lengths on the same scene: Run a 35 mm, 50 mm, and 85 mm prime at the same focus distance and see how object distance and magnification move.
• • Plan a macro build without buying the wrong tube: Compare m without a tube, with a 12 mm tube, and with a 25 mm tube on the same lens.
• • Verify a telephoto framing plan: Pick the focal length that produces the magnification you want at the distance you expect to shoot from.
• • Catch the unphysical setup early: When d < 4*f the square root goes imaginary and the calculator surfaces a 'Not physically realizable' message instead of returning NaN.

The calculator is also a teaching aid because the formula m = h/g forces you to think in terms of object and image distance rather than focal length alone. For macro work, the 'with tube' column is usually the one that drives the decision.

If the focus distance is given in feet or yards instead of meters and you want to keep the mm/m conversion out of your head, the Distance Converter page handles the unit math for any subject-to-sensor distance.

Four factors shift the magnification more than anything else in the formula, and two limitations of the thin-lens assumption are worth knowing up front.

• • The formula assumes a thin converging lens in the paraxial limit, so it overestimates h slightly for very short focal length lenses and for very wide aperture lenses, where spherical aberration starts to dominate.
• • The formula does not include diffraction, sensor pixel size, or aperture-induced depth of field. Treat the magnification as a geometric size ratio and read it alongside depth-of-field and diffraction tables.

If you want more magnification, the cheapest geometric move is to halve the focus distance, the next cheapest is to add an extension tube, and the last is to buy a longer lens.

According to the Wikipedia lens (optics) article, when the focal length f and the total focus distance d between object and sensor are known, the object and image distances are recovered from g = d/2 + sqrt(d^2/4 - f*d) and h = d/2 - sqrt(d^2/4 - f*d), and the magnification is m = h/g

Higher-magnification frames produce larger file sizes, so the Upload Time Calculator page is a useful follow-up when you need to estimate how long the resulting RAW or video files will take to push to a backup server.