Scientific Calculator

A scientific calculator earns its name from four things a basic one cannot do: trigonometric functions, logarithms, powers and roots, and numbers too large or too small to write out. This one takes the whole expression at once, shows it on the small line above the answer while you type, and previews the result before you press equals. Almost every wrong answer people get from a scientific calculator comes from one of three places: the wrong angle mode, an order of operations the calculator reads differently from the person typing, or a precision limit nobody mentioned. This guide covers all three.

The design goes back further than most people assume. Hewlett-Packard introduced the HP-35, its first pocket calculator, on 1 February 1972 at US$395, and it replaced the slide rule and the printed table of logarithms more or less overnight. Texas Instruments followed with the SR-50 on 15 January 1974. The keys on this page, sin, cos, tan, log, ln, x to the y, square root and pi, are the same set those machines established, with inverse trig, a cube root and a remainder key added.

Degrees, radians and gradians: which angle mode to use

The three modes measure the same turn in different units. A full circle is 360 degrees, 2π radians, or 400 gradians. One radian is the angle at the centre of a circle when the arc cut off is exactly as long as the radius, which works out at about 57.2958 degrees. The radian is the SI unit, and it is a pure ratio, arc length over radius, so it has no dimension at all.

• Degrees suit school geometry, triangles, bearings and most trigonometry homework. Set Deg and sin(90) returns 1.
• Radians are what calculus, physics and programming assume. Only in radians is the derivative of sin x exactly cos x, and angular velocity is quoted in rad/s. If a question has π in the angle, it almost certainly wants Rad, where sin(π/2) returns 1.
• Gradians, also called gon, put a right angle at exactly 100. They are used mainly in surveying, especially in Europe, and are a legally recognised unit in the EU and Switzerland even though they sit outside the SI. Most calculators sold today have dropped the mode; it is kept here for the surveyors who still need it.

Inverse trig keys answer in whichever mode is active. With Deg set, sin⁻¹(0.5) gives 30; with Rad set, it gives 0.5236, which is π/6. Press d on a keyboard to cycle the three modes without reaching for the mouse.

Order of operations, and the three places calculators disagree

The standard order is brackets first, then exponents, then multiplication and division, then addition and subtraction, with operations of equal rank worked left to right. Americans learn it as PEMDAS, British and Commonwealth schools as BODMAS or BIDMAS, and Canada and New Zealand as BEDMAS. They are the same rule under different names, so 2 + 3 × 4 is 14 everywhere, never 20. The table above the guide lists every rank this calculator uses. The trouble is in three cases the mnemonics never mention.

Stacked powers. Written by hand, a tower of exponents is read from the top down, so 2^3^2 means 2^(3^2), which is 2^9, or 512. Google and Wolfram Alpha agree. Microsoft Excel and MATLAB work a chain of carets left to right instead and give (2^3)^2, which is 64. This calculator follows the written convention and returns 512.

A minus sign in front of a power. In ordinary algebra, -3^2 means -(3^2), which is -9: the power is done first and the sign applied afterwards. Casio's manuals make the same point with -2^4 = -16 against (-2)^4 = 16. Excel is the famous exception and returns 9. Here the answer is -9. If you mean the square of negative three, type the brackets.

Implied multiplication. The expression 6 ÷ 2(1 + 2) is the one that goes round social media every year, and handhelds genuinely split on it. Casio's fx range gives multiplication with the sign left out a higher priority than a typed × or ÷, so it reads 6 ÷ (2 × 3) and shows 1. Texas Instruments did the same on its early TI-80, 81, 82 and 85, then changed: the TI-83, TI-84 Plus, TI-89 and TI-Nspire families give implied and explicit multiplication the same rank and work left to right, which gives (6 ÷ 2) × 3 = 9. This calculator follows the TI-84 rule and shows 9. Neither answer is a bug. The expression is ambiguous, and the cure is a pair of brackets.

Scientific notation and the EXP key

Scientific notation writes a number as m × 10^n, where the mantissa m is at least 1 and less than 10 and n is a whole number. It exists because numbers like the mass of an electron, 9.10938356 × 10^-31 kg, are unreadable written out in full. Calculators show it in E notation, so Avogadro's constant appears as 6.022E23, meaning 6.022 × 10^23.

The EXP key types that E. To enter 6.022 × 10^23, press 6.022, EXP, 23. For a negative exponent press ± straight after EXP. The E binds to the number it belongs to, so 6.022E23 × 2 behaves exactly like one number times two, which is not true of typing × 10 ^ 23 by hand inside a longer expression. Answers switch to E notation automatically once they reach 10^15 or fall below 10^-9, and they come out with the same E the key types, so an answer can be copied straight back in. Engineers often prefer engineering notation, where the exponent is always a multiple of 3 so it lines up with SI prefixes such as kilo, mega and nano; to get it, move the decimal point by hand.

The function keys in one pass

• log is the common logarithm, base 10: log(1000) = 3. ln is the natural logarithm, base e: ln(e) = 1. To take a log in any other base, divide: log base 2 of 8 is log(8) ÷ log(2) = 3.
• 10ˣ and eˣ undo log and ln respectively.
• x² squares, xʸ raises to any power, and √ and ∛ take square and cube roots. For any other root use a fractional power: the fifth root of 32 is 32^(1/5) = 2. The cube root accepts negatives, so ∛(-27) = -3, while the square root of a negative is undefined in real numbers.
• x! is the factorial, 5! = 120. It needs a whole number of 0 or more.
• mod returns the remainder, 17 mod 5 = 2. % divides the number before it by 100, so 200 × 15% is 30.
• Ans recalls the last answer, and pressing an operator straight after equals carries on from it.

How precise the answer is

Like nearly every web calculator, this one does its arithmetic in IEEE 754 double precision, the number format built into JavaScript. A double stores a 53 bit significand, which gives 15 to 17 significant decimal digits, and any decimal of 15 significant digits or fewer survives the round trip intact. The largest double is about 1.798 × 10^308 and the smallest normal one about 2.225 × 10^-308.

Binary cannot store most decimal fractions exactly. In raw JavaScript 0.1 + 0.2 comes out as 0.30000000000000004, because neither 0.1 nor 0.2 has an exact binary form, and the gap between 1 and the next representable number, called machine epsilon, is 2^-52, about 2.22 × 10^-16. This calculator rounds every displayed answer to 12 significant digits, the figure a typical handheld shows, so that noise never reaches the screen and 0.1 + 0.2 reads 0.3. The rounding is display only: Ans keeps the full value.

Two consequences are worth knowing. Integers are exact only up to 2^53, which is 9,007,199,254,740,992; beyond that the gaps between representable numbers are wider than 1. And 170! is the largest factorial that fits, at about 7.26E306, because 171! passes the 1.798 × 10^308 ceiling, so it returns Math error. If you need 30 or 60 exact digits, use an arbitrary precision tool instead.

Why sin 180° reads 0 here

Ask a naive web calculator for sin(180) in degrees and it often shows 1.2246E-16 rather than 0. The reason is that π itself cannot be stored exactly, so the converted angle lands a hair away from the true half turn. Ask it for tan(90) and it can print a huge number around 1.6E16 instead of admitting the tangent of a right angle is undefined. This calculator checks for exact quarter turns first. At 0, 90, 180 and 270 degrees, and the matching radian and gradian angles, sine and cosine return exact 0, 1 or -1, and tangent at 90 or 270 degrees returns Math error, which is the honest answer. Every other angle is computed normally.

Scientific calculators and 2026 exams

Handheld scientific calculators stay common in schools because phones and laptops are banned in most exam halls. For the digital SAT, the College Board allows a calculator throughout the Math section but not in Reading and Writing, embeds a Desmos calculator with both a graphing and a scientific option in the Bluebook app, and permits any scientific model. For the ACT, four function, scientific and graphing calculators are allowed, students testing online get the Desmos graphing calculator built in, and models with a computer algebra system or a QWERTY keyboard are banned on both tests. Both policies were read on 23 September 2026 and change from year to year, so check the official page before test day. A web page like this one is for homework and practice, never for the exam room.

For jobs this keypad is not shaped for, use the fraction calculator for exact fractions, the percentage calculator for percentage change, the statistics calculator for a whole data set, and the Pythagorean theorem calculator for the sides of a right triangle.