Scientific Calculator Online
Free online scientific calculator for electrical engineers and students: trigonometry, logarithms, powers, roots, complex numbers and phasors. Calculate. Check. Understand.
Complex result
Enter a complex value such as 10+j15 or 230∠30 to see its real and imaginary parts, magnitude, phase angle and phasor diagram.
Working
History
Results you confirm with = appear here. Select one to use its expression again. History stays in this page and is not stored.
Worksheet
Press Add to worksheet to keep a result with its expression, settings and a note of your own. When you are done, print the worksheet or save it as a PDF. The worksheet stays in this page and is not stored, so print or copy it before you close the page.
How to use it
Standard mode is a full scientific calculator: brackets and operator precedence, trigonometry, logarithms, powers and roots, factorials, constants, memory and the previous answer. Engineering mode adds complex numbers, rectangular and polar form, phasor arithmetic and SI prefixes for electrical work. Type on the keyboard or use the keypad. Press Enter or = to confirm a result and add it to the history, and use Add to worksheet to collect results with notes for printing or saving as a PDF.
- Keyboard: type an expression, press Enter to confirm, Escape to clear. Use * and / or × and ÷. Powers are written with ^.
- Functions take brackets, as in sin(30) or sqrt(16). Brackets are not needed for a single value: sin30 and √144 also work.
- Variables: type a name, an equals sign and an expression, as in
f=50, then press Enter. Use the name in later calculations, for example1/(2*pi*f*100u). Names are letters only and are not case sensitive. The stored values appear under the result and are gone when you close the page. - Ans is the last confirmed result. MS, M+ and M− store, add to and subtract from memory, and MR enters it as
mem. - An error is explained in words, for example division by zero, or a square root of a negative number outside Engineering mode.
Functions and keys
| Key | What it does | Example | Result |
|---|---|---|---|
| sin, cos, tan | Sine, cosine and tangent of an angle in the angle mode you choose | sin(30) | 0.5 |
| sin⁻¹, cos⁻¹, tan⁻¹ | Inverse functions: the angle, in the active angle unit | asin(0.5) | 30 |
| atan2 | Angle of the point (x, y) in the correct quadrant, in the active angle unit: atan2(y, x) | atan2(1,-1) | 135 |
| sinh, cosh, tanh | Hyperbolic functions and their inverses (asinh, acosh, atanh) | sinh(1) | 1.175201194 |
| log, ln | Logarithm base 10 and natural logarithm | log(1000) | 3 |
| log₂, logₓ | Logarithm base 2, and to any base: logb(number, base) | logb(81,3) | 4 |
| eˣ, xʸ | Exponential and powers, evaluated right to left | 2^10 | 1024 |
| √, ∛, ʸ√x | Square root, cube root and nth root: root(number, n) | root(32,5) | 2 |
| n! | Factorial of a whole number from 0 to 170 | 5! | 120 |
| nCr, nPr | Combinations and permutations | ncr(5,2) | 10 |
| mod | Remainder, with the sign of the divisor | mod(17,5) | 2 |
| % | Divides by 100 | 200*15% | 30 |
| abs, floor, ceil, round | Absolute value and rounding to a whole number | abs(-7.5) | 7.5 |
| 1/x | Reciprocal of the whole expression | inv(8) | 0.125 |
Every result in this table is calculated by the same engine as the calculator above.
Angle modes
The angle mode changes how trigonometric functions read their input. The same angle gives the same answer in each mode:
| Mode | Full circle | Example | Result |
|---|---|---|---|
| DEG | 360° | sin(30) | 0.5 |
| RAD | 2π rad | sin(pi/6) | 0.5 |
| GRAD | 400 grad | sin(100/3) | 0.5 |
Switching mode does not convert numbers you have already typed. A degree sign written after a value, as in 30°, always means 30 degrees and is converted to the active unit.
Order of operations
| Order | Rule | Example | Result |
|---|---|---|---|
| 1 | Brackets and function arguments | (2+3)*4 | 20 |
| 2 | Factorial, percent and degree sign, applied to the value before them | 3!^2 | 36 |
| 3 | Power, evaluated right to left | 2^3^2 | 512 |
| 4 | Unary minus, so it applies after a power | -2^2 | -4 |
| 5 | Polar angle ∠ (Engineering mode) | 2∠30*3 | 5.19615 + j3 |
| 6 | Multiply and divide, left to right, including a multiplication sign left out | 10/2*5 | 25 |
| 7 | Add and subtract, left to right | 2+3*4 | 14 |
Where a rule could be read two ways, the calculator follows the usual convention for scientific calculators: -2^2 is -4, and 2^3^2 is 2^9. Use brackets when in doubt. A product written without a sign, as in 3(4+5) or 2sin(30), is read as multiplication. The Implicit multiplication setting changes how a product with the sign left out ranks against division: by default 1/2π is (1/2)·π, and the other choice reads it as 1/(2π) so that 1/2πfC means 1/(2πfC). Explicit signs are never affected: 1/2*pi is always (1/2)·π. Two numbers side by side with a space, as in 1 000, are rejected rather than multiplied, so a thousands separator cannot silently change an answer.
Engineering mode: impedance example
Enter an impedance of Z = 10 + j15 Ω and the calculator returns its parts, its magnitude |Z| = √(10² + 15²) and its phase angle θ = tan⁻¹(15/10):
| Real component | 10 Ω |
|---|---|
| Imaginary component | +15 Ω |
| Magnitude | 18.028 Ω |
| Phase angle | 56.31° |
| Representation | 18.028 ∠ 56.31° |
- Rectangular form: Z = 10 + j15 Ω
- Magnitude: |Z| = √(10² + 15²) = 18.028 Ω
- Phase angle: θ = atan2(15, 10) = tan⁻¹(15/10) = 56.31°
- Polar form: Z = 18.028 ∠ 56.31° Ω
More examples, with results shown to 6 significant digits:
| Expression | Rectangular | Polar |
|---|---|---|
| (10+j15)*(5-j2) | 80 + j55 | 97.0824 ∠ 34.5085° |
| 230∠30 | 199.186 + j115 | 230 ∠ 30° |
| 1/(j*2*pi*50*100u) | 0 - j31.831 | 31.831 ∠ -90° |
| 230*(j20)/(10+j20) | 184 + j92 | 205.718 ∠ 26.5651° |
| sqrt(-4) | 0 + j2 | 2 ∠ 90° |
Complex results from the trigonometric, logarithmic, power and root functions are available in Engineering mode, and a negative number under a square root gives an imaginary result instead of an error. Phase angles follow the angle mode and are normally read in degrees. par(Z1, Z2) gives impedances in parallel.
Limits and accuracy
- Numbers are double precision (about 15 to 17 significant digits). Very large or very small results are shown in scientific form.
- Factorials are limited to whole numbers up to 170. Larger values overflow.
- An even root or a non-integer power of a negative number is an error in Standard mode, and a complex result in Engineering mode, using the principal value.
- On a branch cut, such as asin(2), the sign of the imaginary part is a convention. Check it before using it in a design.
- Phase angles are shown between -180° and 180°.
- The calculator is a general mathematical tool. It does not know about units: the unit you choose in Engineering mode is a label on the result, and it is not checked.
Cross-check: 756 reference cases, calculated with Python’s math and cmath modules, written separately from this calculator (they cover each angle mode, inverse and hyperbolic functions, logarithms, powers and roots, factorials, operator order, error cases, complex arithmetic, polar input and SI prefixes), and 14 polar conversions agree with it. The calculator’s own tests also cover the standard values in the table below.
| Test | Expected result |
|---|---|
| sin(30°) | 0.5 |
| cos(60°) | 0.5 |
| tan(45°) | 1 |
| log(1000) | 3 |
| ln(e) | 1 |
| √144 | 12 |
| 5! | 120 |
| 2³ | 8 |
| 1/0 | Error: division by zero |
Frequently asked questions
How does this calculator read what I type?
It uses its own expression parser, written for this page. It does not use eval or run your text as code, and nothing you type leaves your browser. Brackets, operator order and functions follow the usual rules of mathematics.
How do I switch between degrees, radians and gradians?
Choose DEG, RAD or GRAD above the keypad. It sets how sin, cos and tan read their input and the unit of asin, acos and atan results. You can also write the degree sign after a value, as in sin(30°), and it is converted to the active unit.
Why does sin(180) show 0 and not a tiny number?
In degree and gradian mode the calculator uses exact values at multiples of 30 and 45 degrees, so sin(30) is exactly 0.5 and cos(90) is exactly 0. In radian mode a result that is only rounding noise, such as sin(π), is shown as 0.
How do I enter complex numbers and polar values?
Switch to Engineering mode. Write the imaginary unit as j, for example 10+j15. For polar input write the magnitude, the ∠ sign and the angle, for example 230∠30, or type 230<30. The angle follows the angle mode. Results show as rectangular and polar form, with a phasor diagram and the working.
What do k, M, m, µ, n and p do in Engineering mode?
Written directly after a number they are SI prefixes: 4.7k is 4,700, 100u is 100 microunits (0.0001) and 33n is 33 nano. They are not read as prefixes when a letter follows, so 3pi is 3 times pi.
What does the % key do?
It divides the value before it by 100, so 200*15% is 30. It does not add a percentage to a total: 50+10% is 50.1. For 50 plus 10 percent write 50*(1+10%).
How many digits are right?
Calculations use double-precision numbers, which hold about 15 to 17 significant digits. The display rounds to the number of significant digits you choose, 10 by default. Results can differ from exact mathematics in the last digits, for example 0.1+0.2 is shown as 0.3.
How do I use a value again, such as a frequency?
Type f=50 and press Enter. The name f then stands for 50 in every later calculation until you clear it or close the page. Names are letters only, up to 20 variables, and the names of functions and constants such as pi, e, i, j and ans are not allowed (i and j are both the imaginary unit, so i cannot stand for current; use a name such as ia). A name is read as one word, so write f c or f*c, not fc. A variable that holds a complex number needs Engineering mode.
What does the Implicit multiplication setting do?
It decides how 1/2π is read. With the default, a product with the sign left out ranks with multiply and divide, so 1/2π is (1/2)·π. With the other choice the product binds first, so 1/2π is 1/(2π), which is how the reactance formula 1/2πfC is usually meant. Use brackets to be sure.
Does it keep my calculations?
No. The history, the worksheet and any variables are held in the page and disappear when you close it. The Copy link button puts your expression in the link, so whoever opens the link sees the same calculation.
Can I keep my results as a worksheet or a PDF?
Yes. After a result appears, press Add to worksheet. Each entry keeps the expression, the result, the angle mode, the number of digits and any variable values it uses, and you can type a note beside it. Give the worksheet a title, then press Print or save as PDF and choose Save as PDF in the print window, or press Copy as text. The worksheet is built in your browser and is not stored or sent anywhere, so it is gone when you close the page.