Scientific
Trig, logarithms, powers, and constants
One control on this calculator causes more wrong answers than every other key combined: the degree/radian toggle. Enter 30 and press sin in degree mode and you get 0.5. Do it in radian mode and you get −0.988, because 30 radians is a little under five full turns around the circle. Neither result is an error; the calculator answered the question you actually asked.
Everything else is a thin layer over the browser’s native Math library, which is IEEE-754 double precision: about 15 to 17 significant decimal digits, with π carried internally as 3.141592653589793 and e as 2.718281828459045. The display is one notch narrower than the arithmetic: results are printed to 15 significant digits, so the π key reads 3.14159265358979 on screen and e reads 2.71828182845905, while the full values stay in the calculation. Trigonometric and inverse-trigonometric functions, natural and base-10 logarithms, squares, square roots and arbitrary powers are all present.
What is absent is anything symbolic. There is no algebra, no differentiation or integration, no matrices, no graphing, and no complex numbers — √−4 returns an error rather than 2i. This evaluates numbers, not expressions in a variable.
Degrees, radians, and what the toggle converts
The two angle modes differ only in how many units divide a full turn: 360 degrees, or 2π radians. The conversion is radians = degrees × π ÷ 180 and degrees = radians × 180 ÷ π, so one radian is 57.29577951 degrees and a full turn is 6.283185307 radians.
Degrees are the convenient unit; radians are the correct one for calculus and physics. The derivative of sin x is cos x only when x is in radians, and the small-angle approximation sin x ≈ x holds only in radians — sin(0.01 rad) = 0.0099998, whereas sin(0.01°) = 0.000175. Any formula lifted out of a physics or engineering text is in radians unless it explicitly says otherwise, and any surveying, machining or construction angle is in degrees.
Gradians, the third convention where a right angle is 100 units, appear on some European instruments and in older geodetic work. This calculator does not offer them; convert by degrees = gradians × 0.9 first.
The function set, and what each key expects
The keypad. The angle toggle is the first key on the scientific pad; it reads DEG or RAD and flips on each press, and the same word shows as a badge above the display, so the active mode is visible while you work. Brackets are ( and ); the general power key is labelled yˣ; the inverse trig keys are sin⁻¹, cos⁻¹ and tan⁻¹, and each returns an angle in whichever mode is active; π and e are single keys that drop the constant onto the entry line. There are no memory registers, and C clears the expression line along with the entry.
Trigonometry. sin, cos and tan take an angle in the active mode. The inverse functions return an angle in that same mode, and they have domains: asin and acos accept only values from −1 to 1, because no real angle has a sine of 1.5. They also return principal values only — asin(0.5) gives 30°, never 150°, even though both have that sine.
Logarithms. ln is base e; log is base 10. This is the single most common transcription bug when moving a formula between a calculator and code, because in JavaScript, C and Python the function named log is the natural logarithm, the opposite of the calculator convention. For any other base, use the change-of-base identity: log_b(x) = ln x ÷ ln b. Base-2 of 1000 is ln 1000 ÷ ln 2 = 9.9658.
Powers, roots and constants. Square, square root and a general y^x key cover most work; a cube root is y^(1÷3). The π key exists mainly to stop people typing 3.14 and losing four digits of accuracy in a circle calculation.
Two worked problems: a hypotenuse and a roof pitch
Pythagoras. For legs of 6 and 8, c = √(a² + b²). Enter 6, press x² for 36; then + 8, press x² for 64, press = for 100; then √ for a hypotenuse of exactly 10.
Roof pitch. A carpenter’s "6 in 12" pitch rises 6 units for every 12 of run. In degree mode, atan(6 ÷ 12) = atan(0.5) = 26.565°. The rafter for a 12 ft run is then 12 ÷ cos(26.565°) = 13.4164 ft. Check it the other way: √(12² + 6²) = √180 = 13.4164. Two independent routes agreeing to four decimals is a stronger sanity check than either answer alone, and if they disagree the angle mode is almost always the reason.
Logarithms in practice. How many doublings turn $1,000 into $10,000? ln 10 ÷ ln 2 = 2.302585 ÷ 0.693147 = 3.3219 doublings. At 7% a year, one doubling takes ln 2 ÷ ln 1.07 = 10.24 years, so roughly 34 years — which is where the "rule of 72" shortcut comes from.
Exact values to check your angle mode against
| You type | sin in degree mode | cos in degree mode | sin in radian mode |
|---|---|---|---|
| 0 | 0 | 1 | 0 |
| 30 | 0.5 | 0.8660 | −0.9880 |
| 45 | 0.7071 | 0.7071 | 0.8509 |
| 60 | 0.8660 | 0.5 | −0.3048 |
| 90 | 1 | 0 | 0.8940 |
The right-hand column is the giveaway. If sin 30 returns 0.5 you are in degrees; if it returns a negative number close to −1 you are in radians and every angle in the problem is wrong. The degree-mode values 0.5, 0.7071 (√2÷2) and 0.8660 (√3÷2) are worth memorising for exactly this reason.
Where floating point shows through
Some results that should be clean are not. In radian mode sin(π) returns 1.22464679914735 × 10^−16 rather than zero, because the stored value of π is the nearest double to π and not π itself. tan(π÷2), which is mathematically undefined, returns roughly 1.633 × 10^16 for the same reason: the input is a hair away from the true asymptote, so the tangent is merely enormous rather than infinite. Most of the time the effect hides instead: a result short of 1 by one part in 10^16 is inside the rounding of the 15-digit display and prints as a clean 1. The two cases above are visible precisely because they fall outside that window.
Genuine domain errors are reported as errors. The square root of a negative number, the logarithm of zero or of a negative number, and inverse sine or cosine of anything outside −1 to 1 all fall outside the real-valued definitions of those functions. If a physics or electronics formula pushes you into √ of a negative, the answer is complex and needs a tool that handles complex arithmetic, not a different calculator setting.
What this cannot do, and what to reach for instead
This is a numeric evaluator: you give it numbers, it gives you a number. Solving for a variable, factoring, simplifying an expression, differentiating or integrating symbolically, plotting a function, or working with matrices all need a computer algebra system or a graphing tool.
Repeated calculations are the other boundary. Typing 1.07 y^x 30 once is fine; running the same growth factor across thirty separate contribution amounts is not, and belongs in a spreadsheet or in the Compound Interest Calculator, which handles the schedule for you. For plain arithmetic with a visible running expression and no function keys in the way, the Simple Calculator is the lighter tool.
Frequently asked questions
Why does sin(30) give me -0.988?
The calculator is in radian mode and 30 radians is about 4.77 full turns. Switch to degree mode and the same entry returns 0.5.
Is log base 10 or base e here?
log is base 10 and ln is base e. Note that this is the reverse of most programming languages, where a function called log is the natural logarithm. For any other base use ln x divided by ln b.
Why does tan(90) not return an error?
Because it never quite lands on the asymptote. Degree mode converts 90 to radians and gets the nearest double to pi/2, not pi/2 itself, so the tangent comes out merely enormous - about 1.63 x 10^16 - rather than undefined. Radian mode gives the identical figure for pi divided by 2, for the identical reason. Neither is reported as an error; genuine domain errors, such as the square root of a negative, are.
Can it handle the square root of a negative number?
No. Real-number square roots are undefined for negative inputs, and this calculator has no complex-number mode, so it reports an error rather than returning an imaginary result.
How do I calculate a cube root?
Use the general power key with a bracketed exponent: 8, then y^x, then ( 1 / 3 ), then equals, which returns exactly 2. The brackets matter - typing 0.333333 as the exponent instead gives 7.999992, not 8s cube root.
How many digits of precision does it keep?
Two answers, because the arithmetic and the display differ. Internally it is IEEE-754 double precision, about 15 to 17 significant decimal digits, with pi held as 3.141592653589793 and e as 2.718281828459045. On screen every result is rounded to 15 significant digits, so the pi key shows 3.14159265358979 and the e key shows 2.71828182845905. The digits that are not printed are still used by whatever you do next.