Documentation

Start with the example already filled in, then change the values you need. Each calculator explains its equation, shows the steps, and lists the assumptions behind the result.

Electrical engineering

The resistor-divider calculator finds the nominal output and the highest and lowest outputs allowed by the resistor tolerances. It assumes an unloaded output. Hold-up capacitance estimates the capacitor needed when a load draws constant power as the voltage falls. ADC settling estimates how long a single-pole RC input takes to settle within half an LSB.

PCB calculations

For resistance tools, enter lengths and widths in millimeters, and copper thickness or plating in micrometers. Trace resistance uses the copper temperature you enter; it does not calculate self-heating. The via calculator assumes identical vias that share the current equally.

Trace impedance uses one unit for every dimension: millimeters or mils. Measure the clear dielectric gap from the copper face to the reference-plane face. For symmetric stripline, the same gap sits above and below the trace. This estimates transmission-line impedance; it is different from trace resistance and the partial inductance of an isolated conductor.

Stencil ratios help you compare aperture geometry. A ratio alone is not enough to approve a manufacturing process; check the paste and assembly requirements with your supplier.

Entering a matrix

Put one row on each line and separate entries with spaces or commas. You can enter fractions such as 2/3. Matrix operations, RREF, and linear systems use exact fractions and support matrices up to 7×7. Eigenvalue calculations accept real 2×2 or 3×3 matrices and can return complex eigenvalues and vectors.

Writing a function

Use the variables named beside the input: x for root finding and integration, or x and y for Euler and RK4. Write powers with ^ and multiplication with *. For example, enter x^2 - 2 or 2*x. Supported functions include sin(x), cos(x), exp(x), sqrt(x), abs(x), and ln(x); pi and e are also available.

Euler and RK4 allow up to 80 steps. Use a negative step size to work backward. The step size stays fixed during the calculation, so repeat with a smaller step to see how much the answer changes.

Finding roots and estimating integrals

For bisection, choose endpoints with opposite function signs and check that the function is continuous between them. An endpoint that is already a root is accepted too. Newton's method needs a derivative; the secant method needs two different starting guesses. Read the final residual and any convergence warning before relying on the answer.

Integration offers midpoint, trapezoid, Simpson 1/3, and Simpson 3/8 rules. Simpson 1/3 needs an even number of subintervals; Simpson 3/8 needs a multiple of three. Interpolation accepts 2–10 points with different x values. Results outside the supplied x range are extrapolations and can be unreliable, especially with high-degree polynomials.

Reading values and units

Electrical and PCB results choose a suitable unit automatically: for example, 35.27 mF rather than 35,270 µF. Headline values use four significant digits, and worked steps use six. Downloads keep the original calculated values and units.

Extra digits do not make a model more accurate. Matrix operations, RREF, and linear systems use exact fractions within their stated limits; the other solvers use floating-point arithmetic. A residual tells you how closely a result satisfies the equation. A small residual alone does not guarantee an accurate answer, so also check the assumptions and how the answer changes when you vary the inputs or numerical settings.

Saving a calculation

Select Download calculation (.json) to save the inputs, results, and steps on your device. The website does not store your inputs, so save a calculation before leaving the page if you want to keep it. Downloads are records of a calculation; the website cannot reopen them to resume your work.

All Math Workbench tools are free, and no calculator requires an account. For help with a result, see calculator help.