Prompt-cache savings for a shared prefix: cost with and without caching, break-even requests and percent saved.

Rank 2 to 20 models by cost for a workload from your own prices; flags models whose context window is too small.

Forecast monthly and yearly LLM spend from daily requests, tokens and prices, with monthly growth and per-user cost.

Sustainable requests per minute under RPM and TPM limits, job duration for N requests, and concurrency needed.

Milling table feed from rpm, flutes and chip load, or the chip load a given feed produces.

Bolt preload (75 percent of proof) and tightening torque estimate T = K F d for ISO property classes 8.8, 10.9, 12.9.

Sheet-metal bend allowance, outside setback, bend deduction and flat length from angle, radius, thickness and K-factor.

ISO metric thread dimensions: pitch diameter, minor diameters, thread height and tensile stress area.

Tap drill size for metric coarse (M3 to M24) and common inch threads (#4-40 to 1/2-20), with the formula check.

Spindle rpm for a diameter at a surface speed (SFM or m/min), or the surface speed an rpm gives.

Compare realtime and batch API cost for a workload with your discount fraction, and the money saved by waiting.

Rough LLM token estimate of text from characters and words, as a low-high range by content type. Not a tokenizer.

Cost of LLM API calls from input and output tokens and your per-million-token prices, per request and in total.

Metres per pixel, map scale (1:N) and tile width on the ground for a zoom level and latitude.

Metal removal rate for milling (width x depth x feed) or turning (surface speed x feed x depth of cut).

Western zodiac sign and Chinese zodiac animal with element for a birth date, flagging cusp days and lunar-year boundaries.

Convert a tile x/y/z to a Bing Maps quadkey, or a quadkey back to x/y/z, with its parent and four children.

Slippy-map tile x/y/z containing a latitude and longitude, plus the pixel position inside the 256 px tile.

Number of slippy-map tiles covering a lat/lon box for a zoom range, with a rough storage estimate at your average tile size.

Convert latitude/longitude to Web Mercator EPSG:3857 metres, or metres back to degrees, with scale distortion.