Gradient percent and angle from rise and distance, plus climbing rate (VAM) and the time to climb at a given rate.

Starting saddle height from inseam by the LeMond (0.883) and Hamley (1.09) rules, plus the Holmes knee-angle check.

Chain length in links, rounded up to even, from chainstay length and chainring and cog teeth, with the exact figure.

Rolling circumference and diameter for common tyre sizes, or an estimate from rim bead diameter and tyre width in mm.

Render a FEN position as an 8x8 ASCII board (White at the bottom) plus a piece-by-square list.

Best text color (black or white) for a background hex color, with contrast ratios and WCAG AA/AAA results for both.

Classify a chess time control (bullet, blitz, rapid, classical) from base minutes and increment, with estimated length.

File, rank, light or dark colour, 0-63 index, diagonals and mirror squares for a chess square like e4.

Material balance from a FEN: standard 1-3-3-5-9 point totals per side, difference and piece lists.

Parse PGN tag pairs, check the Seven Tag Roster, result token and date format, and count the moves in the movetext.

Squares a knight, bishop, rook, queen, king or pawn reaches from a square on an empty board, with the count.

Distance between two chess squares as king moves, rook moves, bishop moves and knight moves on an empty board.

Gear inches and speed at a cadence for every chainring and cog in a drivetrain, with the range, steps and duplicate gears.

Gear ratio, gear inches, development per pedal turn and speed at a cadence for a chainring and cog on a given wheel.

Rough bike frame size (seat tube cm and S/M/L) from inseam by bike type, with a height-based letter size cross-check.

Cadence needed to hold a target speed in a given gear, and the chainring-to-cog ratio needed for a speed at a cadence.

Evenly spaced color steps between two hex colors, in sRGB or linear light, for charts, heatmaps and gradients.

IANA time zones for a country with UTC offsets and daylight-saving flags at a given moment (default now).

Adjust a text color's lightness just enough to reach a WCAG contrast target (4.5, 3 or 7) on a background, keeping its hue.

Mix two hex colors at a ratio in sRGB or in linear light (physically correct), returning the blended hex.