Scientific calculator

How to use the online scientific calculator

Type the calculation as one line, the way you would write it. Brackets come first, then powers, then × and ÷ from left to right, then + and −: 2 + 3 × 4^2 = 2 + 48 = 50. Angles are in degrees unless you switch to radians, and fractions stay exact: 3/4 − 1/6 = 7/12.

Common calculations and how to type them:

Brackets change the order: (12 + 8) × 3 = 60, but 12 + 8 × 3 = 36, because the multiplication runs before the addition. Add brackets whenever you are unsure how a line will be read.

For trig, match the angle unit to the problem. sin(30) = 0.5 in degrees; in radians, the same angle is sin(pi/6). The inverse sine sin⁻¹, typed asin(0.5), returns the angle 30°. It is not the reciprocal 1/sin(30) = 2.

How does the percent key work?

On its own, 10% is 0.1, so 200 × 10% = 20 and 15% of 240 = 36. After + or −, the percentage is taken of the number before it: 200 + 10% = 220 and 200 − 10% = 180. To add the decimal 0.1, type 200 + 0.1.

To find a percentage change, or what percent one number is of another, use the percentage calculator.

Which math calculator should I use?

An expression has to work out to a number, so a letter such as x has no value. To solve ax² + bx + c = 0 for x, use the quadratic equation solver, and to plot a function, the graphing calculator. To write a very large or very small number in powers of ten, or to apply significant-figure rules, use the scientific notation calculator.

For fraction arithmetic with every step shown, use the fraction calculator. Browse all calculators for money, dates and measurements.

Order of operations: PEMDAS and BODMAS

PEMDAS and BODMAS name the same convention. These are the exact rules, from the tightest binding to the loosest:

Take 8/2(2 + 2), a common test of these rules. The bracket gives 4, then ÷ and × run left to right: 8/2 = 4 and 4 × 4 = 16. If 8 is meant to be divided by 2(2 + 2), type 8/(2(2 + 2)), which gives 1.

The same left-to-right rule makes 1/2pi equal (1/2) × π = 1.5708, not 1/(2π). Type 1/(2pi) for 0.159155. Powers group from the right instead: 2^3^2 = 2^9 = 512, while (2^3)^2 = 64.

A leading minus sign applies after the power, so -3^2 = −9, matching −x² = −(x²) in algebra. To square a negative number, bracket it: (-3)^2 = 9. A minus sign right after ^ belongs to the exponent, so 2^-1 = 0.5.

Implicit multiplication rules

You can leave out × between a number or closing bracket and a name, function, opening bracket or root sign: 2pi, 3(4 + 5), 2 sin(30), (1 + 2)(3 + 4) and 4√9 all multiply. This has the same priority as ×, which is why 8/2(2 + 2) is 16.

A digit multiplies only after a closing bracket or a factorial: (1 + 2)3 = 9 and 4!/(2!2!) = 6. Two bare numbers such as 2 3 are an error, as is the x in 2x, because x is not a defined name.

A function name without brackets takes only the next number and its power. In radians, sin 2pi means sin(2) × π = 2.8566, while sin(2pi) = 0. In degrees, sin 30^2 is sin(900°) = 0; type sin(30)^2 for (sin 30°)² = 0.25.

Three typing details change a result without any error:

• E-notation. 2e3 is 2 × 10³ = 2000 and 2e+1 is 20, but 2e + 1, with spaces, is 2 × e + 1 = 6.4366.
• Commas. Outside brackets, 1,000 is one thousand. Inside a function a comma separates arguments, so max(1,000, 2) reads as max(1, 0, 2) and returns 2.
• Suffixes. k, M, B and T multiply by 10³, 10⁶, 10⁹ and 10¹², and lakh and cr by 10⁵ and 10⁷: 2.5M is 2,500,000 and 3 cr is 30,000,000.

Degrees, radians and gradians

A full turn is 360°, 2π radians or 400 gradians, so each unit converts to the others by a fixed ratio. Calculations start in degrees.

The usual mistake is a textbook angle in the wrong mode: sin(30) is 0.5 in degrees but −0.988032 in radians, where it means 30 radians. Inverse functions answer in the current unit, so atan(1) is 45 in degrees and 0.785398 in radians.

deg() and rad() convert a number between radians and degrees without changing the mode. In degree mode, sin(rad(30)) takes the sine of 0.5236 degrees and returns 0.0091384. The graphing calculator always works in radians.

In degrees, angles whose sine or cosine is 0, ±1/2 or ±1, or whose tangent is ±1, come out exact: sin(150) = 0.5 and cos(90) = 0. Others, such as sin(45) = 0.70710678…, carry 50 significant digits. tan(90) has no value and gives an error.

Exact fractions and 50-digit decimals

Arithmetic, whole-number powers, percentages, repeating decimals such as 0.(3), and abs, round, min, max and mod keep an exact fraction. A fraction of up to 18 digits is shown beside the decimal: 100/7 = 14.2857142857.

Roots, logarithms, trig, π, e and non-whole powers switch to 50 significant digits and drop the fraction: sqrt(4)/3 shows 0.666666666667, while 2/3 stays exact. Answers are rounded to 12 significant figures by default, so sqrt(2)^2, held as 1.999…9, reads 2.

Decimal arithmetic also rounds ties the way they look on paper: round(2.675, 2) = 2.68. Binary floating point stores 2.675 as 2.67499999…, which is why Python's round() documentation gives 2.67. Halves round away from zero: round(-2.5) = −3.

Scientific functions and constants

Function arguments go in brackets. Trig results below assume degree mode.

The remainder takes the sign of the divisor, so -7 mod 3 = 2, where JavaScript's % gives −1. (-8)^(1/3) = −2, but (-4)^0.5 has no real value; use the complex number calculator. The permutations and combinations calculator explains what nCr and nPr count.

Chained answers and exactness

A result reused in the next calculation carries its 50-digit decimal, not its fraction. So 1/7 followed by × 7 shows 1 but holds 0.999…98, while 1/7*7 typed as one line is exactly 1. Keep a calculation on one line when you need an exact answer.