Image scale calculator

What image scale means and what the response contains

Image scale, often called plate scale in classical astronomy, is the angular sky size covered by one detector pixel once light is focused by a telescope or camera lens. Under the small-angle approximation the angle in radians is the linear pixel pitch divided by the effective focal length when both lengths share the same unit; converting that angle to arcseconds and expressing the pitch in micrometres and the focal length in millimetres yields the familiar textbook formula S equals two hundred six point two six five times p_μm over f_mm. That single number tells you how finely the sky is sampled: values much smaller than typical local seeing oversample the atmosphere, while values much larger undersample fine structure and waste resolution. This calculator returns the normalized pixel_size and pixel_size_um you supplied, the focal_length and focal_length_mm, the primary image_scale and image_scale_arcsec_per_pixel fields in arcseconds per pixel, an arcsec_per_mm companion for field-of-view planning, the fixed arcsec_factor of two hundred six point two six five, a unit string arcsec/pixel, the method tag plate_scale_206265, the precision used, and a short formula reminder. There is no ray-trace, no atmospheric model, and no random sampling of optical modes: the engine either builds exact floating-point S inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing pixel size or focal length, non-finite values, magnitudes above the documented ceilings, non-positive pixel size, and zero or negative focal length—because division by f is undefined.

How pixel size and focal length are read and how S stays reproducible

Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong scale. Pixel size must likewise be positive so the product has a physical meaning for a real detector element. The preferred fields are pixel_size for the detector pitch in micrometres and focal_length for the effective focal length in millimetres, but aliases pixel_size_um, pixel_um, and p for the first, and focal_length_mm, fl, and f for the second, are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Focal length must be strictly positive and non-zero: if f is zero, negative, or negative zero, the request fails with invalid_input because image scale S equals two hundred six point two six five times p over f is undefined for a zero or negative focal length. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for the numeric outputs, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the plate-scale formula yourself.

Where image scale fits in study, observing, and software

On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with telescope-resolution or angular-size tools when you need related astronomy steps, and with other physics endpoints when you are building a small lab of free, deterministic science helpers.