Scientific Calculator

You pick one operation, supply x (and y for powers), and get a result to 15 significant digits. The seven operations are sine, cosine, tangent, natural logarithm, common logarithm to base 10, square root, and x raised to the power y. Each one is evaluated over the real numbers only, so inputs outside a real domain are refused with a reason rather than returned as a nonsense value: logarithms require x greater than zero, square root requires x at or above zero, zero raised to a power needs a positive exponent, and a negative base needs an integer exponent, because a fractional power of a negative number is complex. Tangent is refused exactly at its poles, where cosine is zero. The angle unit is the setting that quietly ruins answers, and it is the reason this page makes you choose explicitly rather than defaulting silently. NIST Special Publication 330 states that the coherent SI unit of plane angle is the radian, with 360 degrees equal to 2*pi radians; the conversion used here is radians = degrees x pi / 180. Feed 30 to a calculator set to radians and you do not get 0.5. You get roughly -0.988, because 30 radians is about 4.77 full turns around the circle and lands somewhere entirely different. Nothing about that answer looks broken - it is a perfectly plausible number between -1 and 1 - which is exactly why the mistake survives all the way into finished spreadsheets and homework. Every trigonometric result here is labelled with the unit it assumed so you can catch the mismatch at a glance. Underneath, the arithmetic avoids binary floating point entirely. The decimal library used across this site deliberately omits trigonometric methods, and reaching for the browser's built-in sine would first collapse your decimal input into a binary double, throwing away precision before the calculation even starts. Instead, sine and cosine are computed from the power series published in the NIST Digital Library of Mathematical Functions (DLMF 4.19.1 and 4.19.2), accumulated in a private 50-digit decimal context, after reducing the angle into the range from -pi/2 to pi/2 so the series converges quickly and large angles do not lose digits to cancellation. Tangent is their quotient, per DLMF 4.14.4. Logarithm, root and power use the decimal library's own implementations. Pi is carried to 80 decimal places. Results keep all 50 working digits internally and are rounded exactly once, at the display boundary, to 15 significant digits. One further refinement: in degrees, the cardinal angles 0, 90, 180 and 270 are returned as exact values rather than computed. Any finite decimal is only an approximation to pi, so passing through the conversion would turn sin(180 degrees) into a tiny nonzero residue and tan(90 degrees) into an enormous but finite number instead of undefined. Handling those four angles exactly keeps the identities you expect actually true. Because the calculation runs on the server from the URL's query parameters, every result is a link you can share or bookmark, and the page works with JavaScript switched off. If your problem is proportional rather than transcendental, the percentage calculator covers percent of, share of, and percentage change, and for repeated growth over time the compound interest calculator applies the exponent for you rather than making you build it here.