Math & Engineering

This tool converts a value from one unit to another within the same category by first turning it into a common base unit, then translating that base value into your target unit — for most categories that means multiplying by a fixed conversion ratio, while temperature uses linear offset formulas instead (like Celsius to Fahrenheit) since those scales don't share a zero point. Results update live as you type, so it's worth double-checking that both the "from" and "to" units belong to the category you actually intend, since switching category resets the unit lists.

Each shape uses its own standard formula: circles and spheres rely on πr² (and 4/3πr³ for a sphere's volume), rectangles multiply width by height, a triangle's area is half its base times height, and cylinders and cones combine circular cross-sections with height to get volume and surface area. For the triangle, entering all three side lengths additionally unlocks the perimeter, since base and height alone aren't enough to determine the length of the slanted sides. Surface area figures include every face of the solid, so a cylinder's result covers both circular ends plus the curved side, not just the "wrapper."

This calculator evaluates whatever expression you build with the buttons or type directly, following standard order of operations, and supports trigonometry, natural and base-10 logarithms, powers, and roots on top of basic arithmetic. Trig functions respect the DEG/RAD mode shown above the display, so switching modes changes how sin, cos, and tan interpret their input — a common source of "wrong" answers if you forget it's set to the other one. The M+ / M- / MR / MC buttons work like a physical calculator's memory register, letting you accumulate a running total separately from whatever's currently on screen.

Standard deviation and variance here are calculated as sample statistics (dividing by n−1 rather than n), which is the appropriate choice when your numbers are a sample drawn from a larger population rather than the entire population itself — it slightly inflates the result to correct for the bias of estimating from a subset. Mode reports every value tied for the highest frequency, and shows "no unique mode" when every value appears exactly once. The histogram groups your data into 8 equal-width bins between the minimum and maximum, which is useful for spotting skew or clustering that the summary numbers alone won't reveal.

Linear equations are solved by simple algebraic rearrangement (x = −b/a), while quadratics use the quadratic formula, which hinges on the discriminant b² − 4ac: a positive discriminant gives two distinct real roots, zero gives one repeated real root (the parabola's vertex touches the x-axis), and a negative discriminant means the parabola never crosses the x-axis, so the two roots are complex conjugates. The chart plots the parabola itself, so you can visually confirm whether — and where — it intersects the x-axis before trusting the numeric roots.

Addition, subtraction, and multiplication combine matrices A and B entry-by-entry or row-by-column respectively, while transpose simply flips A across its diagonal, swapping rows for columns. The determinant is computed directly from the entries (the ad−bc shortcut for 2x2, cofactor expansion for 3x3) and is a single number that summarizes the matrix: a determinant of zero means the matrix is singular and has no inverse, which matters if you're using these matrices to solve a system of equations elsewhere. Multiplication requires both matrices to be the same size here, and note that A × B generally isn't the same as B × A.