Engineering & Matrix Calculator
Complex impedance · SEM · scientific functions · matrix operations
Scientific & engineering calculator
Insert a constant, then use * for multiplication (e.g. 2*c0). Hover for its value and units. Constants are expressed in SI.
Case matters: m = milli, M = mega. u, µ and μ all mean micro. Press a prefix after a number, e.g. 47 + u.
rad(x) converts degrees to radians.Xc(f,C) = 1/(2πfC) · Xl(f,L) = 2πfL · Zc(f,C) = -iXc · Zl(f,L) = +iXl. Arguments can contain SI prefixes or calculations, and these functions also work in every matrix cell.Number format, output prefix and decimal places (Auto or 0–9) affect live displayed answers and cell previews only—not input values or calculation precision. Auto follows the selected number format; in SEM, Auto chooses prefixes in steps of 1000. Choosing a fixed prefix scales results into that prefix regardless of the selected number format. Phase angles are never SI-scaled.
Matrix workspace
Use functions, SI prefixes, rectangular/polar complex numbers and full arithmetic expressions in any matrix cell. Click a cell to make it the keypad target.
Matrix calculations & output
Enter a matrix expression below. Its answer appears in the dedicated output box on the right.
Change matrices A–D above, or type expressions such as inv(A)*B, 2*A or A^2. Complex numbers, polar notation and SI prefixes work here too.
Insert an operator into a matrix cell
Click a matrix cell first, then click an operator below. The operator is inserted at the cursor. These same operators also work in the main calculator.
Clicking a sample replaces the contents of the selected cell. Parentheses determine grouping; multiplication requires * except in a number such as 3i.
Try these calculations
Supported cell and calculation operators
+Addition-Subtraction / negative values*Multiplication/Division^Integer powers, including negative powers||Parallel combination of two or more values( )Parentheses / groupingiImaginary unit, e.g. 3+2iRectangular and polar complex numbers
Enter 3+4i, 5∠53.130102°, 10k∠30° or mixtures such as (5∠30°)+(2+3i). The ∠ operator uses the selected angle unit; adding ° explicitly means degrees even in radians mode. Compound angles should be grouped, e.g. 5∠(pi/2) in radians mode. Select Rectangular, Polar or Both independently for the quick answer and matrix output. Each matrix input cell always shows evaluated rectangular and polar previews underneath its expression. In Both mode, a matrix shows two separately bracketed representations of the same complex-valued result. arg(z) returns the phase in the chosen angle units; abs(z) and mag(z) both return the magnitude. Calculation precision is never rounded to the displayed form.
Output formats
Normal: 4700.000; Scientific: 4.700e+3; Engineering: 4.700e+3 (exponent divisible by 3); SEM: 4.700k. All 24 prefixes are valid input; SEM Auto output uses the engineering series spaced by 10³, so 0.01 appears as 10.000m. The Output SI prefix dropdown can instead force any prefix—for example, 100k becomes 0.100M with Mega (M) selected at 3 decimal places. Fixed prefixes override Normal, Scientific and Engineering number notation for displayed numeric values, but not phase angles. Base units (no prefix) forces unscaled decimal output. Outside the official SI range, SEM falls back to engineering notation. Uppercase A–D designate matrices in the main expression.
How parallel works
a||b||c = 1 / (1/a + 1/b + 1/c). Parallel combinations accept real and complex numbers. If one impedance is exactly zero, the parallel equivalent is zero. A parallel combination with zero total admittance and no zero impedance is undefined (division by zero). || has lower precedence than +, -, *, /, and ^. For example, 10||20+5 means 10||(20+5); use (10||20)+5 if that is what you intend.
For full-matrix expressions, A||B combines corresponding entries in equally sized matrices. A||10 combines each entry of A with 10. Regular A*B remains matrix multiplication (not elementwise multiplication).
Impedance and reactance functions
Xc(f,C) returns positive capacitive reactance; Xl(f,L) returns positive inductive reactance; Zc(f,C) returns negative imaginary impedance; Zl(f,L) returns positive imaginary impedance. Frequency f is in Hz, C is in farads, and L is in henries. Frequencies must be nonnegative, capacitances positive, and inductances nonnegative; capacitive functions require nonzero frequency. These functions take two real scalar arguments and work in standalone calculations and matrix cells.
Other matrix functions
det(A) determinant, inv(A) inverse, transpose(A), conj(A) complex conjugate, conjT(A) conjugate transpose, rref(A) reduced row echelon form, trace(A), eye(3), solve(A,B) for AX=B, abs(z), mag(z), real(z), imag(z), and sqrt(z) (complex scalar square root). Constants pi, e, and i are supported.
Arbitrary-base logarithms: Use logn(value,base), for example logn(32,2) = 5 or logn(81,3) = 4. Select Functions → logₙ, enter the number first, then a comma and the base. The existing log(value) calculates base 10, ln(value) uses base e, and log(value,base) remains supported.
Constants menu: Common physical and mathematical constants are available under Constants. Insert names such as c0 (light speed), kB (Boltzmann), hP (Planck), eps0 (permittivity), mu0 (permeability), g0 (standard gravity) and phi (golden ratio). These are in SI units; constants marked approximate reflect published rounded reference values. Use explicit multiplication such as 2*c0 or hP*500T.
Scientific functions include ans (previous stored answer), sin/cos/tan (and inverses), hyperbolic functions, natural/common logarithms, exp, arbitrary scalar powers, factorial (!), percent (%), nCr/nPr, and statistics such as mean, median, standard deviations and variances. Trig honors DEG/RAD. Saved quick-calculation history retains the exact rectangular and polar display text from the time each calculation was stored, even if formatting settings change. The editable Note column remains visible in every Quick Output mode and is saved alongside each calculation. An output restore button inserts the stored displayed value without replacing the current expression; for matrix outputs it inserts a saved(n) reference to the archived matrix. History is stored locally in your browser when storage is permitted. Supports matrix sizes 1×1 through 10×10. Each cell must evaluate to one scalar number. Results use floating-point arithmetic and are rounded for display. The formula you enter remains visible and is reevaluated whenever you calculate. All calculation mathematics still run locally in your browser. The optional pretty-print editor uses the MathLive library from a CDN and needs internet access to initialize; Plain text mode works without it.