System of equations.

Using the math editor

Write one equation per row, with one equals sign. Terms can go on either side, in any order. Fractions, powers, and subscripts appear as you type.

/

Make a fraction.

^ · _

Enter a power or subscript.

Right arrow

Move out of a fraction, power, or subscript.

Enter

Move to the next equation, or add a row.

Use Add equation for another row and × to remove one. You can paste multiple equations directly into a row, separated by new lines or semicolons; they replace that row.

Names & multiplication

Greek letters such as θ (theta), φ (phi), α (alpha), and ω (omega) work as variables, constants, or free variables. Use the math keyboard, type their names, or paste the symbols. Subscripts such as θ_1 work too. π remains the built-in constant; µ after a number remains the micro prefix.

Names are case-sensitive. Multi-character names stay together, except for a leading lowercase i or j (the imaginary unit).

Use F_1 for F₁. Subscripts are names, not calculations. Typing an operator such as +, −, *, /, or = automatically leaves the subscript. You can also use the right arrow.

Use * between names: R*x multiplies R by x, while Rx is one name. A number can go directly before a name: 2FA means 2*FA.

Constants and free variables

Open Constants above the equations and choose Add constant. Type the whole definition in one math field, such as R = 100/2. Use a single name before the equals sign; fractions and subscripts display as you type. Press Enter for another constant.

Here R is fixed at 50, so only x is an unknown. Values can use fractions, functions, complex numbers, and constants defined in earlier rows.

Choose Add free variable and enter just a name, such as omega. Later definitions can use it: L = 2m, then Z = j*omega*L. Solving Z*I = 10 gives I in terms of omega. Free variables stay symbolic and may cancel out. Symbolic solving supports systems linear in the dependent variables; parameter values excluded by a denominator or a solving step are shown with the result.

Use distinct names. The built-in names i, j, pi, e, and function names are reserved. Add up to 20 constants. Clear all removes constants and equations.

SI prefixes

Attach a prefix to a number: 10k = 10,000, 4.7M = 4,700,000, 220m = 0.220, 47u or 47µ = 0.000047, and 100n = 0.0000001. Prefixes are case-sensitive.

Use 10*k to multiply by the variable k. This applies to any prefix name: use 2*y for twice the variable y. Names such as k_1 remain variables. Use j*1k for j × 1000. Prefixes work in constants too; units such as volts and ohms are not parsed.

Choose Engineering notation to display results with SI prefixes. Scientific and engineering notation are alternative display modes.

Complex numbers

Both i and j represent the imaginary unit.

3 + 2j

Real and imaginary parts

j10i_1

Means j * 10 * i_1

An i or j directly before a number or name is the imaginary unit: jIx means j*Ix, iIx means i*Ix, and i1 means i*1. Use i_1 for a variable with a numeric subscript.

Polar numbers

Enter a magnitude followed by <angle or ang(angle). 20<30 means 20ang(30). Use parentheses for an angle expression, such as 20<(30+15). For example, 10ang(-90) has magnitude 10 and angle −90°.

Completed polar entries display with ∠. Typing 15<20I_5 inserts multiplication: 15∠20 · I_5. To include a product in the angle, use parentheses: 15<(20I_3). Angles display ° in degree mode, which is the default for new systems. The angle switch applies to polar inputs as well as trig functions. Polar notation works in equations and constant values.

Functions & angle units

Use parentheses, such as sin(x) or sqrt(4).

Trigonometry

sin · cos · tan

Roots & magnitude

sqrt · abs

Exponential & logs

exp · log · ln
Both logarithms are natural logarithms.

Built-in constants

pi · e

The Radians / Degrees switch is always available. Degrees is the default for new systems; the setting applies to trigonometric functions and polar inputs.

Solving & copying values

Choose Solve system, or press ⌘ / Ctrl + Enter. You can use up to 20 equations and 20 unknowns. After changing an equation, constant, or angle setting, solve again to update the result.

Choose complex or polar form, a limit of 1–15 significant digits, and Automatic, Scientific, or Engineering notation above the results. Unnecessary trailing zeros are omitted. Polar angles use the angle mode of the solved system. These settings change the display, not calculation accuracy. For solution families, they apply to numeric coefficients. Use the copy icon beside a solution to copy its displayed value or expression; polar values copy as magnitude followed by ang(angle). Free variables have no copy icon.

Nonlinear solutions are approximate. Search options let you choose real-only or real and complex solutions, and supply starting values. The search may miss roots and does not describe continuous solution families.

Complex logarithms, square roots, and noninteger powers use their principal values.

Choosing free variables

For a linear system with infinitely many solutions, the result separates Dependent variables from Free variables.

Drag a dependent variable onto the free variable you want to swap with. You can also select a dependent variable, then select a free variable.

The solutions update after a valid swap. Some choices cannot vary independently; the app will explain when a swap is not possible. Choose Reset to automatic to restore the automatic selection.