Choose an instrument using
Layout preset above the rule , then adjust its appearance and scale order here. Use Programme JSON for custom scales and saved layouts.
Each graduation mode shows its own options; settings for both modes are remembered. Fully adaptive chooses complete, round-number subdivisions for each continuous scale; Balanced is a good starting point. Conventional applies the shared choice to C/D and W; W uses twice the effective length. The 10-inch choice retains the documented W pattern. Calculations and chemical reference marks are unchanged; custom tick lists require an explicit opt-in.
Edit face
Drag a scale by its dotted grip to reorder it or move it to another rail. The stacked arrows, or Up/Down on a focused grip, move one place and cross to the adjacent rail at an end. Left/Right moves between rails; Home/End moves to the first/last row; Escape cancels a drag. Undo beside Add scale reverses up to 100 scale edits, including removals. Loading a preset or programme, or reloading the page, clears this history. Ctrl/Command+Z works while an editor grip or button has focus.
Programme JSON
Custom expressions use a restricted mathematical language; they cannot execute JavaScript. Arithmetic, powers, parentheses and approved Math functions are supported. For an expression scale, pos receives x and returns 0..1; value receives p and returns the scale value. Built-in programmable types also include root , loglog , foldedLog , foldedInverse , trigonometric and hyperbolic mappings, and pythagorean .
Apply JSON
Use current programme
Export JSON
Import JSON
Pointer magnifying loupe
Enable 2.5× loupe above the rule, then move the mouse or hovering pen over either face. The lens renders the actual graduations and cursor at the larger size using fresh text and strokes, not enlarged screen pixels, including during a drag or keyboard nudge. It does not change the scale coordinates, the instrument magnification or the keyboard step. After four seconds without pointer movement or a keypress, the lens fades out; move the pointer or press a key to restore it immediately. Holding a key keeps it visible. The lens also hides when the pointer leaves the rule. Press M over a focused motion control or rule to toggle it; Escape switches it off. Touch devices without hover can use the ordinary Magnification selector instead.
Keyboard and fine positioning
Tab or click into the Slide or Cursor grip, then use Left/Right (or Down/Up) to move that control. Choose a Keyboard step slider stop without losing motion focus. Keys 1 , 2 , 3 and 4 select Faster (0.005), Normal (0.001), Fine (0.0005) and Very fine (0.0001) while the rule or a grip is focused. Tab and Enter/Space also activate each button and return you to your last motion control. Alt divides the selected step by ten; Page Up/Down uses ten steps. Home/End selects the limits. The small arrow buttons use the same step.
With the instrument focused, S selects the slide and C selects the cursor. Arrows then move the selected part; clicking or dragging a part selects it too. Shift plus an arrow on the rule temporarily moves the slide. On a focused grip, arrows always control that grip. Keyboard shortcuts leave the JSON editor and menus alone.
Faster, Normal, Fine and Very fine mean 0.005, 0.001, 0.0005 and 0.0001 of the graduated length. Alt plus Very fine reaches 0.00001. Position displays normally use four significant digits; Extended decimal precision shows these finer changes with six decimal places, even when movement is less than a screen pixel. These are positional fractions, not scale readings. Exact positions are saved without display rounding; the step setting is session-only.
Page appearance
The Light, Dark and Solarised buttons at the top change the page, controls, readouts and editor, not the instrument. Instrument style in Scale layout remains independent. Page theme is remembered in this browser when storage is available and included as the default in a saved standalone copy; it is not part of Programme JSON.
Pickett Model 14 and constant marks
Load Pickett 14 U.S. Military / Artillery for a general log-log face and a degree/mil trigonometric face. There are 6400 mils per turn; these are not milliradians. The black/red angle numbers are complementary or supplementary readings on shared ticks. The short opposite-angle scales are not stretched to full width. Original end extensions are omitted; this is a mathematical reconstruction, not a fire-control calculator.
Hover over a constant tick or label to see its value and meaning, including through the cursor glass. The arithmetic c gauge is sqrt(4/pi), the circle-diameter factor, not the speed of light . Euler's e, pi, folded indices and special conversion marks have their own explanations. A radiation T index is a movable reference, not a fixed temperature. Escape dismisses a tooltip. Custom ticks and gauges can supply a title; anchors can supply anchorTitle.
Pickett square and cube roots
Load Pickett N3 or N4 and select Front or Both sides. The square-root branches meet one common line. The cube-root bank has an unruled upper branch and a back-to-back middle/lower pair. Both number modes use this construction. Previously saved layouts are retained; use Load preset to adopt the current arrangement.
At D = 6.4, the cube-root branches read about 1.85664, 4 and 8.61774, for 6.4, 64 and 640 respectively. For a positive number N = m × 10k , with 1 ≤ m < 10, set D to m. For an order-n root, choose branch 1 plus the nonnegative remainder of k divided by n, then multiply its reading by 10floor(k/n) . This works for negative exponents too. The gutter digit-count reminders apply to positive integers.
The root branches have independently positioned round-number graduations; they are not reciprocal log-log pairs. All branches increase to the right and use black ink. In the library, PICKETT_SQRT and PICKETT_CBRT add complete movable banks; the generic roots, fifth roots and Faber-Castell W scales remain independent.
Pickett-style fifth roots and powers
Choose Pickett-style fifth roots and powers in Layout preset, then Load preset. This is a mathematical extension, not a historical model. PICKETT_FIFTH_ROOT adds five branches as one bank: an unruled upper branch and two back-to-back pairs, each with a shared line. F5_PAIR adds black x5 and red x−5 on a single set of ticks.
For N = m × 10k , set C/D to m. Choose branch 1 plus the non-negative remainder of k divided by 5; multiply its reading by 10floor(k/5) . At D = 3.2, branch 2 reads 2, the fifth root of 32. For 0.00032, the same branch reads 2; divide by 10 to obtain 0.2. The gutter digit reminders apply to positive integers.
At C/D = 2, the power pair reads 32 and 0.03125 ; their product is 1. The legacy F5I is unchanged and reads 100000/x5 instead. The front uses fixed groups aligned with D; the back uses movable groups aligned with C. Each group can be moved, removed or restored with Undo as one item.
Chemical scales (Hemmi 257 / Flying Fish 1017)
Load Hemmi 257 for its chemical back, or Flying Fish 1017 for its chemical front. Choose Both sides for cross-face work. These are different presets, with their own scientific faces and photographed row arrangements. The calibrations are modern educational models, not a photographic or certified historical reproduction.
Ch A-M / N-Z: 52 element and 18 group/reference marks align with fixed D on the scientific face. Underlined symbols use D × 1, plain symbols D × 10, overlined symbols D × 100. Hover a visible symbol for its value. Readouts identify the nearest mark; they do not interpolate an atomic weight. Representative CIAAW 2024 values are used; Ra[226] is explicitly a mass-number convention.
M1 / Xw and M2 / X (Flying Fish: Mz / Xz and M / X): each row packs a mass setting on its left and a fraction scale on its right. Align M2 with M1, keeping the same decimal rescaling for both. For a 20% by mass ammonium-sulphate solution, align M2 = 1.8 under M1 = 13.21, set the cursor to Xw = 0.2, and read X ≈ 0.033. Xw and X are fractions, not percentages. Density substitution gives volume fractions only under the additive-volume assumption.
Temperature: T F and T C (plus T K on the Hemmi) convert a common 100-1000 K range. They share the slide: conversion between them works at any slide setting. Reset the slide to align them with C/D on the other face.
Pressure: the common six-decade coordinate covers 0.001-1000 kgf/cm² absolute. The paired row reads mmHg absolute below one atmosphere and atm above it. The additional Hemmi row reads inHg vacuum below one atmosphere and psi gauge above it. Gauge/vacuum zero uses 101325 Pa, not the ambient pressure at your location. Boundary values of the two segments refer to the same absolute pressure.
tw: read equilibrium temperature against the fixed pressure rows, independently of the slide. IAPWS correlations cover ice below the triple point and liquid-water/steam above it, from -20 °C to the critical point at 373.946 °C. No steam saturation state exists above that endpoint.
F(t): air is on the left, CO2 on the right. Align the initial gas temperature on F(t) to the initial absolute pressure on P; move the cursor to the final pressure and read the final temperature on the same gas segment. These are reversible, fixed-composition ideal-gas calculations using NIST heat-capacity fits, not compressor-design or real-gas predictions. Air means 79% N2 / 21% O2, valid here from 200-1000 K; CO2 covers 298.15-900 K. An off-scale result is not extrapolated.
Flying Fish 1017 notes
The chemical face includes the near-unity LnI−2 and Ln−2 ranges omitted from the Hemmi layout. The back has LnI−1, LnI0, LnI1, A1; moving lg, T/cot, S/cos, CI, C; and fixed D, Ln1, Ln0, Ln−1. Ln and LnI are exponential log-log scales, not the ordinary logarithm.
The shared chemical functions use the same documented modern mass, pressure, water and ideal-gas models as the Hemmi study. They do not claim identical historical engraving. Original scale extensions, the full historical symbol repertoire and unverified gauge constants are not reproduced. See docs/FLYING_FISH_1017.md in the source package for the photographic evidence and exact mapping convention.
Built-in scale library
Using the slide rule
Drag the middle slide to set the alignment. Drag the glass cursor to read all scales at the hairline. On a classic multiplication setup, align C 1 over a D number, then read products by moving the cursor to another C number and reading D.
Side, Flip side and Both sides are grouped above the rule, before Magnification. Flip with the button, either labelled end border, or F while the rule or a position grip has focus. Flip is unavailable when both faces are visible or the programme has only one face. The highlighted Both sides button returns to the selected editing face when clicked again. Their slide and cursor positions stay linked. In that view, Edit face selects which layout you are changing. The two faces are shown upright, not mirrored. Reset positions, beside Cursor appearance, centres the cursor and aligns the slide indexes.
Full-width workspace: the Layout preset chooser is above the instrument, which uses the available page width. About preset reveals the selected preset description; Load preset applies the choice to both faces. Magnification includes 75% for a smaller view. Scale layout and JSON controls are below it; their own columns adapt to the screen. The Scale layout and Back to rule links jump between the two, and Focus rule hides the editor without changing the graduation width.
Expanded roots: write the radicand as N = m × 10^k , with 1 ≤ m < 10. For an n-th root, choose branch (k mod n) + 1 , put the cursor at m on D, and read the root mantissa on that branch. Example: 32 = 3.2 × 10^1, so 5R2 reads 2 over D = 3.2. A, K, and x⁵ provide the corresponding power scales.
Log-log: LL0 through LL4 cover values above 1; LL00 through LL04 cover values below 1. Pickett paired and Syncro LL± rows use one shared graduation: the black number is above one and the red number immediately below it is its exact reciprocal. The N3 rows are natural-exponential; the N4 rows use Pickett's base-10 geometry.
Compact scale numbering: primary numerals are tucked beside their long ticks. When a label cannot fit cleanly to the right, suitable multi-digit labels are divided around the tick. Turn the option off to restore centred-above-tick numbering. A custom scale can opt out with "compactLabels": false .
Decimal precision: labels and readouts normally show four useful significant digits, with trailing decimal zeros omitted: P's 0.994987… becomes 0.995, and LL01's 0.990049833… becomes 0.99. Values below one use ordinary significant digits, including reciprocal log-log values. On log-log and hypotenuse scales between one and two, useful digits describe the excess above one, so LL0's 1.001000500… becomes 1.001001. Extended decimal precision restores the detailed display. This changes only displayed numbers; calculations, tick positions and saved settings retain their precision.
Trig and hyperbolic: S, COS, T1, T2, ST, and P cover circular functions. SH1, SH2, TH, H1, H2, and CH provide split hyperbolic-function ranges. Load the Trigonometric or Hyperbolic preset for a less crowded working face.