A phasor / complex-number calculator built for AC circuit analysis, with a GeoGebra-style two-pane layout and a live phasor diagram. Ordinary calculators cannot even type phasor notation; this one is built around it.
一个为交流电路分析而生的相量与复数计算器，采用 GeoGebra 风格双栏界面，右侧实时绘制相量图。 普通计算器连相量记号都打不出来，这个工具就是围绕它设计的。
- Type phasors the way textbooks write them —
220\angle 30\degree,3+4j,220e^{j30\degree},5(\cos 53\degree + j\sin 53\degree). - Name things —
U=220\angle 30\degree\text{V}, thenI=U/Z. Subscripts work:U_1,X_{L}. - See it — every visible object is drawn as an arrow; phase angles get an arc marker; drag an arrow tip to change the value.
- Get the numbers you need — modulus, argument, real part, imaginary part, conjugate, both RMS and amplitude forms.
| Four input forms | polar, rectangular, exponential, trigonometric (mix them freely in one expression) |
| Named variables | definitions resolve in any order — I=U/Z may come before U and Z |
| Auto-naming | an expression you did not name becomes A, then B, … Z, A1; a name is reused once its object is gone |
| Names as you write them | U1, I2, T0 are read as subscripts (U_1, I_2, T_0), and so are U_1 and X_{L} |
| Functions | \abs \arg \conj \Re \Im \polar \rms \peak \om \freq \pf \todeg \torad, sin cos tan, asin acos atan atan2, ln log log2 exp, powers, n-th roots, floor ceil round |
| Symbol keyboard | three labelled groups — symbols, units, functions — with the function group foldable; hovering a key explains it with a worked example |
| Keyboard shortcuts | Ctrl+Alt+R root, A angle ∠, D degree, F fraction, J imaginary unit, P π, W ω, E e^x, B brackets, S subscript, C conjugate, M modulus, G argument, T unit label — they type into whichever input box has focus. Each key shows its letter in the corner, and hovering it spells the whole combination out |
| Phone layout | on a narrow screen the diagram moves to the top and the algebra pane becomes three swipeable tabs - Input (the box and the symbol keyboard), Formulas (the object list) and Result (result, comparison and equations). The splitter between the diagram and the tabs can be dragged (double-click restores the default share), rows get ↑/↓ buttons instead of mouse dragging, and every control is sized for touch. A wide screen is completely unaffected. On a phone the field's own keyboard is hidden in favour of this app's: it carries every symbol, unit and function, and keeps a fixed height so the pane never jumps |
| Typography | every value - the numbers under each formula, the result card, the status line and the diagram's ticks and labels - is set in the same LaTeX face the formulas use, so the notation matches. Buttons, menus and hints stay in the UI sans face, and the diagram's tick/label face is shared by the canvas and the SVG export |
| Motion | one restrained vocabulary: dialogs fade and rise 6px in 160ms and fade out in 120ms, new rows rise in, deleted rows sink away, keys flash on press. prefers-reduced-motion switches all of it off |
| Reorder the list | drag an object row up or down to change its place (or select it and press Alt+↑/↓). The order is what the sum polygon chains in, and it is saved with the project |
| Rebindable shortcuts | ⚙ Settings lists every action with its combination: rebind it (press the new one), switch one off, reset one or all back to the defaults. Bindings travel in the project file and can be undone |
| Export and import | project .json (everything, or only the selected object), data table .csv (bilingual header, full precision, UTF-8 with a BOM so Excel opens it by double-click) and the diagram as PNG (1×–4×, transparent background) or SVG vector. Drop a .json or .csv anywhere on the window to import it |
| Live diagram | grid, axes, coloured arrows, labels, phase-angle arc, optional sum polygon, PNG export |
| Direct manipulation | drag a tip to edit the phasor, wheel to zoom, drag the background to pan, double-click to fit |
| Edit again | double-click an object to load its own source back into the input box |
| Recall input | press ↑ in an empty input box to walk back through what you typed before |
| Copy a result | click any line of the result card to put that number on the clipboard |
| Compare two quantities | pick A and B: A/B is the impedance when A is a voltage and B a current, A·conj(B) is the complex power, plus Δφ and cos Δφ |
| Worked examples | five classic setups (series RLC, power factor, three-phase star, parallel branches, a KVL loop) load with one click |
| Undo / redo | every change, including settings, angle-unit switches and the convention conversion |
| Never lose work | the project is saved in the browser as you type, and can be exported / imported as JSON |
| Angle units | degrees (default) or radians, switchable at any time |
| Phasor convention | RMS (default) or amplitude, with an explicit convert all action |
| Bilingual UI | 中文 / English, switchable at runtime |
| About dialog | the ⓘ button shows the version, the repository and what the app is built on |
| Linear equations | an equation card solves 2x+6=0 or a system 3x+4y=10; x-y=1 (up to three unknowns, complex coefficients), shows the decimal and the exact fraction, substitutes the answer back, and stores every unknown as a phasor you can draw |
| Engine | mathjs for evaluation, MathLive for input |
Drag the tip of an arrow to set a new value. Shift keeps the magnitude and only
changes the angle, Alt keeps the angle and only changes the magnitude, and the
15° snap toggle rounds the angle to a multiple of 15°.
The object's expression is rewritten to match, in the same form you typed it.
Turn on sum in the graphics toolbar and the visible phasors are also drawn
head-to-tail, with the resultant labelled Σ = …. That single picture covers
both laws:
- KVL — around a loop the drops add up to the source. Load the Series loop
KVL example:
U_R = 60∠0°,U_L = 80∠90°,U_C = 40∠−90°, and the chain closes onU = 60 + 40j = 72.11∠33.69°. - KCL — at a node the currents sum to zero, so hide everything except the branch currents and the resultant should land on the origin.
The Equations card at the bottom of the algebra view solves first-degree equations, with a system separated by semicolons:
| What you type | What you get |
|---|---|
2x+6=0 |
x = -3 |
3x=1 |
x = 0.333333, exact 1/3 |
3x+4y=10; x-y=1 |
x = 2, y = 1 |
(3+4j)I1+2I2=10; 2I1+(5-j)I2=0 |
a complex pair — mesh analysis, in one line |
Z*I=U (with Z and U already defined) |
I = U/Z |
Up to three unknowns. The answer is shown as a decimal and, when it is a simple ratio, as an exact fraction; every equation is then substituted back with its residual, and each unknown is stored as a phasor object — so it appears in the algebra view, can be dragged in the diagram, and can be used by later expressions.
It refuses to guess: a quadratic (x^2=4), a product of unknowns (xy=6), a
contradictory system (x+y=1; x+y=2), a system that is not independent, or more
than three unknowns all produce a sentence explaining what is wrong instead of an
answer.
On Windows, just double-click start.bat. It installs the dependencies and
builds the app the first time (that needs the network once), then serves it at
http://localhost:4173/ and opens your browser. Keep its window open while you
use the app; start.bat build forces a rebuild after you change the code.
If the app is already being served on that port, it simply opens the browser
instead of starting a second copy.
By hand, the app is a static site — everything under dist/ is the whole program:
npm install
npm run dev # development server
npm run build # type-check + production bundle into dist/
npm run preview # serve the built bundle
npm test # unit testsThen open the printed URL.
The same code also builds a self-contained window with Tauri v2, so there is no browser and no server to keep open:
npm install
npx tauri build --no-bundle # -> src-tauri/target/release/phasor-lab.exe
npx tauri build # also produces an NSIS installerThe executable embeds the whole front end; it only needs the WebView2 runtime,
which ships with Windows 10/11 (and is installed by Edge). Building it needs the
Rust toolchain plus the MSVC build tools once. The installer
(…\bundle\nsis\Phasor Lab_<version>_x64-setup.exe, ~1.7 MB) installs for the
current user only, and it is not code-signed — Windows SmartScreen will ask
for confirmation the first time you run either file.
| What | How to type it |
|---|---|
| Polar | 220\angle 30\degree or 220\angle 30 (bare number = current angle unit) |
| Rectangular | 3+4j |
| Exponential | 220e^{j30\degree} |
| Trigonometric | 5(\cos 53\degree + j\sin 53\degree) |
| Definition | U=220\angle 0\degree\text{V} — the trailing unit is a display label |
| Several at once | U=10;Z=2;I=U/Z |
| Modulus / argument | \abs(Z), \arg(Z) |
| Conjugate | \overline{Z} or \conj(Z) |
| Any phasor from parts | \polar(220, 30) |
| Angle of a ratio | \atan2(y, x) |
| Amplitude ⇄ RMS | \peak(x), \rms(x) |
| Angular frequency | \om(50) = 314.16, and back with \freq(314.16) = 50 |
| Power factor | \pf(53.13\degree) = 0.6 |
| Explicit angle conversion | \todeg(\pi) = 180, \torad(180) = π |
| Logarithms and powers | \ln(x), \log(x) (base 10), \log2(x), \exp(x), 2^10, \sqrt[3]{8} |
| Rounding | \floor(2.7), \ceil(2.1), \round(2.5) |
| Grouping | \left( ... \right) — the ( ) key inserts it with the caret inside |
| Auto-named | 220\angle 30\degree with no name becomes A=220\angle 30\degree |
| Subscripts | U_1 or just U1 — a single letter followed by digits is a subscripted name (U1 = U₁, T0 = T₀). 3+j4 (imaginary unit) and 2e3 (a number) are unaffected |
A trailing \text{...} group is a display label, not part of the number:
U=220\angle 0\degree\text{V} shows as 220 V. Any label works (\text{\Omega},
\text{k\Omega}, \text{\mu F}, or something entirely your own), and it never
affects the arithmetic.
The angle sign takes a magnitude on its left. When the left side is itself a
phasor, it is rotated instead: A\angle 30\degree is A turned 30° further
(A · 1\angle 30\degree). For a plain magnitude the two readings coincide, so
220\angle 30\degree is unchanged, and -5\angle 30\degree still lands on the
opposite ray. \polar(r, \theta) always uses the size of r, which is what
"modulus and angle" means.
Three rules, and everything else follows:
- Expressions are evaluated in radians internally.
- A bare number in an angle position (
220\angle 30,\sin 30) is read in the current angle-unit setting; the°sign always means degrees. - Angle-valued results (
\arg,\asin,\atan, …) come back in the current angle unit, so they compose with bare values —\phi = \arg(Z)followed by220\angle \phidoes what you expect in either unit.
Changing the angle unit re-reads every stored expression, so 220\angle 30 really
does change meaning between degree and radian mode (that is the point).
A run of letters is a product of single-letter variables (abc = a·b·c), except
for known function words (abs, arg, conj, …) and known constants
(pi, e, i, j, plus Greek names like omega). U_1 and X_{L} are single
symbols.
npm test runs 328 unit tests: the LaTeX converter, the whole documented syntax
table (four input forms, the angle model, naming, unit labels, the convention
factor and twelve rejected inputs), the session model including undo/redo,
auto-naming and project round-trips, the diagram geometry, the two-phasor
comparison, the keyboard tables, and every shipped example (which is evaluated
and compared against the textbook answer).
The UI itself is checked in a real browser: a headless-Chrome harness drives the
page through its public handle, asserts on computation results and DOM state,
samples canvas pixels to confirm the arrow and the sum polygon are drawn where
they should be, and exercises drag-to-edit, zoom, pan, hide/delete, undo/redo,
input recall, copy-to-clipboard, the example picker, the comparison card, the
keyboard groups and their hints, auto-naming, the help dialog, a phone-width
layout, reload persistence and project export/import (131 checks). It also checks
that nothing rendered from LaTeX leaks its own source - across the key labels,
the hint examples, the algebra rows and the input box itself - and that hovering
every key moves nothing on the page, which is how several keyboard keys got
caught showing \abs( instead of the symbol.
Any current Chromium, Firefox or WebKit build. MathLive ships its own fonts, so no network access is required at runtime.
MIT — see LICENSE.
Bundled third-party software: mathjs (Apache-2.0), MathLive (MIT), KaTeX fonts (MIT).