The calculator can evaluate mathematical expressions involving Basic Arithmetic, Advanced Math, Units of Measure and Conversions, and Physical Constants. Let’s see details about each of these.
1. Basic Arithmetic
Compute expressions containing standard mathematical symbols. The following table lists operators that come between the two numbers on which they operate, e.g., to multiply 2 times 3, use 2 * 3.
|+||Addition||[ 11.81 + 12.14 + 14.23 ]|
|-||Subtraction||[ 68 - 11 - 21 ]|
|*||Multiplication||[ 5 * 6 * 7 ]|
|/||Division||[ 432 / 5 ]|
|^ or **||Exponentiation (raise to a power of)||[ 3^4 ] or [ 3**4 ]|
|% of||Percent||[ 12% of 85.12 ]|
|mod or %||modulo (the remainder after division)||[ 17 mod 6 ] or [ 17 % 6 ]|
|the nth root of||calculates the nth root||[ 4th root of 16 ]; [ cube root of 109 ]; [ square root of 42 ] or [ sqrt(42) ]|
Note: To do multiplication, you must include the * symbol; [ 3 * 4 ] will be calculated, 3 4 won’t.
2. Advanced Math
Compute results involving mathematical constants, such as e, pi, i (the square root of -1), and mathematical functions. The following table lists just some of the functions built into Google’s calculator.
|sin, cos, tan, sec, csc, cot, etc.||Trigonometric functions (arguments are assumed to be in radians)||[ cos(pi/5) ]; [ cosine(pi/5) ]|
|arcsin, arccos, arctan, arccsc, etc.||Inverse trigonometric functions||[ arccos(.3) ]|
|sinh, cosh, tanh, csch, arsinh, arccsch, etc.||Hyperbolic functions||[ cosh(5) ]|
|ln||Logarithm base e||[ ln(17) ]|
|log||Logarithm base 10||[ log(17) ]|
|lg||Logarithm base 2||[ lg(17) ]|
|exp||Exponential function||[ exp(17) ]|
|!||Factorial||[ 7! ]|
|choose||x choose y calculates the number of ways of choosing a set of y elements from a set of x distinct elements||[ 7 choose 4 ]|
The following table lists just a few of the commonly used mathematical constants known to the calculator function.
|Name and description||Example|
|base of the natural system of logarithms||[ e ]|
|pi, the ratio of the circumference to the diameter of a circle||[ pi/7 ]|
|imaginary number, i, which represents one of the two square roots of -1||[ i^2 ]|
|Euler’s constant, gamma||[ e^gamma ]|
3. Units of Measure and Conversions
Compute expressions involving different units. By default, units are converted to and results expressed in meter-kilogram-second (mks) units. Many units have both long and short names. Use whichever name you prefer.
|Type of Units||Examples|
|Currency||Australian Dollars (AUD), British pounds (GBP), Euros, US Dollars (USD)|
|Mass||kilogram or kg, grams or g, grains, pounds or lbs, carats, stones, tons, tonnes|
|Length||meters or m, miles, feet, Angstroms, cubits, furlongs|
|Volume||gallons, liters or l, bushels, teaspoons, pints|
|Area||square kilometers, acres, hectares|
|Time||days, seconds or s, centuries, sidereal years, fortnights|
|Electricity||volts, amps, ohms, henrys|
|Energy||Calories, British thermal units (BTU), joules, ergs, foot-pounds|
|Power||watt, kilowatts, horsepower or hp|
|Information||bits, bytes, kbytes, etc.|
|Quantity||dozen, baker’s dozen, percent, gross, great gross, score, googol|
|Numbering systems||decimal, hexadecimal or hex, octal, binary, roman numerals, etc. Prefix hexadecimal numbers with 0x, octal numbers with 0o and binary numbers with 0b. For example: 0×7f + 0b10010101.|
Here are calculations that involve units.
Convert from one set of units to another by using the notation, x units in y units.
- [ three quarters of a cup in teaspoons ]
- [ 84.3 degrees Fahrenheit in degrees Celsius ]
- [ 124 lbs in kg ]
- [ 124 lbs in stones ]
- [ 75 mph in kph ] or
- [ 75 mph in km/h ]
Warning: When your query includes "e;Calories"e; with a capital "e;C,"e; Google returns kilocalories called "e;calories"e; by nutritionists.
Convert from one numbering system to another.
- [ 1700 in hex ] or [ 1700 in hexadecimal ]
- [ 64 in binary ]
- [ LVII in decimal ]
In many cases, you can also get the conversion factor between units:
4. Physical Constants
Note: Sometimes Google’s calculator interprets lower case letters different from upper case letters.
|Long Name||Shorthand Notation||Click the Link for the Approximate Value|
|atomic mass units||amu||[ amu ] or [ atomic mass unit ]|
|Astronomical Unit||au||[ au ] or [ astronomical unit ]|
|Avogadro’s number||[ N_A ] or [ Avogadro’s number ]|
|Boltzmann constant||k||[ k ] or [ Boltzmann constant ]|
|electric constant, permitivity of free space||[ epsilon_0 ]|
|electron mass||[ m_e ] or [ electron mass ]|
|electron volt||eV||[ eV ] or [ electron volt ]|
|elementary charge||[ elementary charge ]|
|Euler’s constant||[ Euler’s constant ]|
|Faraday constant||[ Faraday constant ]|
|fine-structure constant||[ fine-structure constant ]|
|gravitational constant||G||[ G ] or [ gravitational constant ]|
|magnetic flux quantum||[ magnetic flux quantum ]|
|mass of each planet and of the sun||[ m_mars ], [ m_earth ], [ m_uranus ], …, [ m_sun ]|
|molar gas constant||[ molar gas constant ]|
|permeability of free space||[ permeability of free space ]|
|Planck’s constant||h||[ h ] or [ Planck’s constant ]|
|proton mass||[ m_p ] or [ proton mass ]|
|radius of each planet and of the sun||[ r_earth ], [ r_pluto ], …, [ r_sun ]|
|Rydberg constant||[ Rydberg constant ]|
|speed of light in a vacuum||c||[ c ] or [ speed of light ]|
|speed of sound in air at sea level||[ speed of sound ]|
|Stefan-Boltzmann constant||[ Stefan-Boltzmann constant ]|
Here are some calculations using built-in constants.
5. Using Parentheses
Parentheses (( )) can be used whenever they’ll serve to make complicated expressions unambiguous, and also sets of parentheses can be used within parentheses. Don’t use brackets ([ ]) for grouping.
The following are tips from Google’s online help for the calculator, which can be found on the web at www.google.com/help/calculator.html.
You can force the calculator to try to evaluate an expression by putting
an equals sign (=) after it. This works only if the expression is arithmetically
computable. For example, 1-800-555-1234= (a US phone number followed by an
equals sign) will return a result, but 1/0= will not.
Parentheses can be used to enclose the parts of your expression that you want evaluated first. For example, (1+2)*3 causes the addition to happen before the multiplication.
Feel free to experiment with the calculator as not all of its capabilities are listed here.