10 free math and science calculators — scientific, fractions, percentages, triangle solver, random number generator, quadratic formula, statistics, grades, unit conversion & number systems.
The difference between a calculator and a solver is whether it shows the reasoning. The tools here lean towards solvers: the quadratic tool reports the discriminant, not just the roots, because the sign of b² − 4ac tells you what kind of answer to expect before you compute it. For 2x² + 5x − 3 the discriminant is 5² − 4 × 2 × (−3) = 49, a perfect square, which guarantees two clean rational roots — and indeed x = 0.5 and x = −3. A negative discriminant would have meant no real roots at all.
Fractions are a genuine representation problem rather than a convenience. A third cannot be written exactly in decimal, so any calculator that converts to decimal first accumulates error, and adding thirds repeatedly will eventually fail to give a whole number. A fraction calculator keeps numerator and denominator as integers throughout and reduces only at the end, which is the only way to stay exact.
Statistics carries the subtlest trap on this page: dividing by n or by n − 1. For the set 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, and the standard deviation is 2.0000 if those eight values are your entire population but 2.1381 if they are a sample drawn from something larger. The second is always the bigger number, because a sample understates the spread of the population it came from, and the n − 1 correction compensates for exactly that bias.
Number-base tools convert by repeated division, keeping remainders in reverse order — which is why 156 becomes 10011100 in binary and 9C in hexadecimal, and why hex is the compact way to read binary: each hex digit stands for precisely four bits.
Percentages are where confident arithmetic goes wrong most often, because two operations that look symmetrical are not. Add 20 per cent to 100 and you get 120; take 20 per cent off 120 and you get 96, not 100, because the second percentage is taken from the larger number. Recovering the original requires a rise of 25 per cent, not 20. The same asymmetry is why a stock that falls 50 per cent must double to break even.
The related trap is the percentage point. A rate moving from 4 per cent to 5 per cent has risen by one percentage point, but by 25 per cent in relative terms, and the two figures describe the same event. Both readings are correct and they are not interchangeable, so the percentage tool reports the change and the base it was taken from rather than a single number.
The triangle solver handles a case that has two right answers. Given two sides and an angle that is not between them, the law of sines can be satisfied by two different triangles: with a side of 7, a side of 10 and a 40-degree angle opposite the 7, the unknown angle is either 66.7 degrees or 113.3 degrees, giving third angles of 73.3 and 26.7 degrees. Both are geometrically valid. A solver that silently returns one of them has answered a question you did not ask, which is why this is the ambiguous case and why it is worth knowing before you trust the output.
Grade tools are most useful run backwards. Averaging what you already have is simple arithmetic; the question people actually bring is what the final exam has to be. With an 88 per cent average across coursework worth 70 per cent of the module and a target of 90 per cent overall, the final must reach 94.7 per cent — and seeing that figure early is more useful than seeing it afterwards.