Electrical Engineering Calculator

What is a phasor?

A phasor is a complex number that stands in for a sine wave. In an AC circuit every voltage and current swings at the same frequency, so the only things that tell two waves apart are how big they are and how far one runs ahead of the other. A phasor packs both into one number. Written in polar form, 10∠30 means "10 volts, leading by 30 degrees." Written in rectangular form, the same wave is 8.66 + j5.

Charles Steinmetz worked this out in the 1890s, and it is still the first thing every AC circuits course teaches. The trick is that once waves become complex numbers, resistors, capacitors and inductors all become impedances, and Ohm's law works again. A 1 kΩ resistor is 1000. A capacitor with 1 kΩ of reactance is -j1000. An inductor with the same reactance is +j1000. Add them, divide them, put them in parallel, and the answer tells you both the size and the phase of what comes out.

The catch is the arithmetic. Adding is easy in rectangular form, multiplying is easy in polar form, and real problems need both, so you spend half your time converting. This Electrical Engineering Calculator does the converting for you. Type the expression the way your textbook writes it, and the answer shows up in both forms at once.

How to use the Electrical Engineering Calculator

1. Type an expression. The cursor is already in the box. Rectangular numbers look like 3+4j, j4 or 4i. Polar numbers look like 10∠30; if your keyboard has no ∠ key, 10<30 and 10@30 mean the same thing.
2. Use + - * / as usual, ^ for whole-number powers, and || for two impedances in parallel.
3. Put SI prefixes straight onto numbers: p n u m k M G. 4.7k is 4700 and 100n is 0.0000001.
4. Pick Degrees or Radians. The choice covers the angles you type and the angle in the answer.
5. Read both forms side by side. Each has its own Copy button, and it copies exactly what you see.

There is no Calculate button. The answer updates as you type. If you stop halfway through, say at 3+, the last good answer stays on screen, dimmed, and the error only shows once you stop typing for a moment.

That's the whole flow. No menu of forty formulas to pick from first, no account, no trial. Most engineering math online comes in one of three shapes: a hub page that makes you choose a single-formula calculator before you can type, a homework site that paywalls the steps behind a "free trial" that turns into a monthly charge, or a desktop suite sold per seat. The newest shape bundles an AI tutor into a subscription to read your phasor for you. You don't need a contract, or a model, to multiply two complex numbers.

The formulas behind phasor math

Every phasor calculator runs on four relationships. Here they are, with a + jb as the rectangular form and r∠θ as the polar form.

Start with the classic: 3+4j has r = √(9 + 16) = 5 and θ = atan2(4, 3) = 53.13°. The calculator shows 3 + j4 and 5 ∠ 53.13°. Going the other way, 10∠30 gives a = 10 × cos 30° = 8.66 and b = 10 × sin 30° = 5, shown as 8.66 + j5. Multiply two polar numbers and the rule is visible in the answer: (10∠30)*(2∠15) is 20 ∠ 45°.

A worked example: an RC filter at 1 kHz

Take a 1 kΩ resistor and a 100 nF capacitor at 1 kHz. The capacitor's reactance is 1 / (2πfC). There is no π key, so type the number:

1/(2*3.1416*1k*100n) → 1592 ohms.

In series, the pair is 1k - j*(1/(2*3.1416*1k*100n)), which comes back as 1000 - j1592 and 1880 ∠ -57.86°. The negative angle tells you the load is capacitive. Current leads voltage.

Now drop the frequency to the point where the reactance equals the resistance, 1 kΩ each. That is the filter's corner. Feed it 10 V and take the output across the capacitor with the voltage-divider rule:

10∠0 * (-j1k)/(1k - j1k) → 5 - j5 and 7.071 ∠ -45°.

That is 70.7% of the input, the familiar -3 dB point, lagging by exactly 45°. One line, both forms, and the textbook result falls out of it.

Common parallel impedance results

Parallel impedance is where hand calculation hurts most, because the formula needs a complex multiply, a complex add and a complex divide. The table below puts a 1 kΩ resistor beside different reactances. Every row is what the Electrical Engineering Calculator returns for the expression shown.

Two patterns are worth noticing. First, with a resistor and one reactance, the parallel magnitude is always smaller than either part, and the smaller the reactance, the closer the angle gets to ±90°. Halve the capacitive reactance from 1 kΩ to 500 Ω and the angle swings from -45° to -63.43°.

Second, look at the last row. An ideal inductor and capacitor with equal reactance cancel in parallel, so the tank looks like an open circuit and only the resistor is left. Take the resistor away and there is no finite answer at all: 100 || -100 divides by zero, and the calculator tells you so instead of printing a huge number.

The same operator works on plain resistors too. 220 || 330 is 132, which saves you the reciprocal dance from DC class.

Common mistakes and limitations

Most wrong answers here come from the input, not the arithmetic. These are the ones worth checking first.

Parallel binds tighter than plus

|| sits at the same level as * and /. So 1k + j500 || -j2k means 1k + (j500 || -j2k), which is 1000 + j666.7. If you meant the whole branch in parallel with the capacitor, bracket it: (1k + j500) || -j2k is 1231 - j153.8, or 1240 ∠ -7.125°. Different circuit, very different answer.

The angle toggle covers your input too

Switch to Radians and 10∠30 means 30 radians, not 30 degrees. It comes back as 1.543 - j9.88. If an answer looks rotated for no reason, check the toggle first.

What it doesn't do

• No variables, memory or history. Each expression stands alone, so copy the answer you want to keep.
• No π, no square roots, no conjugate. Powers have to be whole numbers, because a complex number has more than one root and picking one quietly would be wrong half the time.
• No mesh or nodal solver. It evaluates one expression; you set up the circuit.
• No reactance helpers yet. Type 1/(2πfC) or 2πfL out by hand, as in the example above.

Related calculations

The Electrical Engineering Calculator covers the AC side. For the DC side, the Ohm's law calculator solves voltage, current, resistance and power from any two of them.

Once you know a load's current, the voltage drop calculator tells you whether the wire run can carry it without losing too much on the way.

For power conversions, kW to amps and kVA to amps handle the single-phase and three-phase formulas, and the transformer calculator finds full-load current on both windings.

If you'd rather work in radians but think in degrees, the degrees to radians converter does the switch on its own.

All of them work the same way. Open the page, type, read the answer. The tool works the same whether you're a second-year student checking homework, a technician on a service call, or an engineer sanity-checking a filter before ordering parts. And 10% of every dollar Microapp earns goes to charity, off the top, audited quarterly.

Frequently asked questions

Why is 4.7K refused when 4.7k works?

Because prefixes are case-sensitive, and the SI symbol for kilo is a lowercase k. Capital K isn't a prefix at all, so the Electrical Engineering Calculator says it can't read 4.7K rather than guess. Case matters elsewhere too: 1m * 1k is 1, but 1M * 1k is 1e9.

Can I write 2(3+4j) without the star?

No. There is no implicit multiplication, so 2(3+4j) is refused. Write 2*(3+4j), which gives 6 + j8, or 10 ∠ 53.13°. The same goes for j(2): write j*2 or just j2.

What does a negative angle mean for an impedance?

It means the load is capacitive: current leads voltage. A positive angle means inductive, where current lags. The 1 kΩ resistor and 100 nF capacitor at 1 kHz come out at 1880 ∠ -57.86°, so that circuit is mostly capacitive.

Why does a balanced three-phase sum show 3.202e-15 instead of 0?

Because cos 120° and sin 120° can't be stored exactly in binary, so (10∠0)+(10∠120)+(10∠240) leaves a crumb of about 3e-15. The calculator clears crumbs smaller than a billionth of the answer, but when the whole answer is that crumb, there's nothing to compare it against. Read anything around e-15 next to inputs of 10 as zero. Subtracting a phasor from itself, like (10∠30)-(10∠30), does give an exact 0.

How do I calculate current from a voltage and an impedance?

Divide, just like Ohm's law. A coil with 50 Ω of resistance and 62.83 Ω of reactance (200 mH at 50 Hz) on a 230 V supply is 230∠0 / (50 + j62.83), which comes back as 2.864 ∠ -51.49° amps. The current lags the voltage by 51.49°, as an inductive load should.

Can a negative number be a polar magnitude?

Yes, through the minus sign in front. -10∠30 flips the whole phasor half a turn and shows 10 ∠ -150°. Brackets around the magnitude, like (-10)∠30, aren't read, because a polar literal starts with a plain number.

Does it keep my expressions or need an account?

No to both. The Electrical Engineering Calculator saves nothing between visits and has no signup. Everything runs in your browser, so copy the answer before you close the tab.