Web map scale calculator

What map scale means on a Web Mercator basemap

When zoom or DPI is zero or negative the geometry is undefined for a map viewer, so this capability rejects non-positive zoom and non-positive DPI with invalid_input instead of inventing a scale.

How to call the API and what comes back

Zoom must be strictly positive and at most thirty; DPI must be strictly positive and at most one million; latitude must lie between minus ninety and ninety inclusive. Send a JSON body with three required finite numbers: zoom (aliases z and zoom_level), latitude (aliases lat and y), and dpi (aliases screen_dpi and resolution_dpi). On success the response echoes rounded zoom, latitude, and dpi, publishes earth_radius_m as six million three hundred seventy-eight thousand one hundred thirty-seven and tile_size as two hundred fifty-six, returns meters_per_pixel as the ground resolution, scale_denominator as the representative N (rounded to the nearest integer when absolute value is at least one), scale_ratio as the string one-colon-N, formula as the closed expression used, message as a short English summary, and steps as an ordered substitution trace you can show in worksheets or assertions. Failed validation—missing fields, non-finite numbers, latitude out of range, zoom above the published cap, DPI above the published cap, or non-positive zoom or DPI—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

Prefer ninety-six DPI when you want the common CSS / browser reference pixel; use seventy-two only when you are matching legacy print assumptions; use the true device pixel ratio times ninety-six when you care about physical phone or retina panels. Fractional zoom is allowed because modern map engines interpolate between integer tile levels—pass ten point five when the camera sits halfway between ten and eleven. Near the poles the cosine factor collapses meters-per-pixel and therefore N; that is correct for Web Mercator, not a bug, though real apps often clamp latitude near eighty-five degrees for tile coverage. Prefer this capability when you already have zoom, latitude, and DPI and only need one-to-N; if your source is a printed map without a zoom number, measure ground and map distances directly instead. Keep zoom at or below thirty so two-to-the-zoom stays finite in IEEE double precision on the Worker and in the browser. When teaching, pair examples: zoom ten at New York with ninety-six DPI yields a city-scale denominator; the same zoom at the equator is slightly smaller N because cosine is larger; a deliberate dpi of zero or zoom of zero demonstrates the hard invalid_input path. This landing targets people searching for a web map scale calculator, zoom to scale denominator, or Mercator map scale online; it is not a geodesic distance tool, not a print layout engine, and not a tile URL builder. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send non-positive DPI. Round-trip checks are easy: recompute cos of latitude in radians times the published initial resolution divided by two to the zoom, multiply by DPI over zero point zero two five four, and confirm the integer denominator matches the published scale_denominator within a unit of ordinary rounding.