Desmos Scientific Calculator User Guide

Welcome to the Scientific Calculator!

You can use the Desmos Scientific Calculator to evaluate expressions, define functions, compute with complex numbers, work with lists, and much more.

If you have questions that aren’t answered here, send us an email at support@desmos.com.

Scientific Calculator showing the keyboard with trigonometric, exponential, and other math function buttons below an empty expression input field. Screenshot.

 

Settings and Key Features

Accessibility Accessibility: For a list of keyboard shortcuts, press Ctrl + / (Windows) or Cmd + / (Mac).

Calculator Settings

Click Settings Settings to open the Settings menu. From there, you can increase text size, turn on Reverse Contrast and Braille Mode, and toggle on Complex Mode.

Use the Keypad

Use the on-screen keypad to enter numbers, symbols, and functions. The keypad has three tabs: main for common operations, abc for letters, and func for additional functions. Toggle between RAD and DEG to switch between radians and degrees (the default).

You can enter a fraction by typing / or clicking ÷ on the keypad. Both will display your expression as a fraction. For example, typing 1/2 or clicking 1 ÷ 2 will display as the fraction \(\frac{1}{2}\).

Click clear to clear the current expression. This button only appears when there are two or more expressions with content. From a blank expression or when there’s only one expression, you can click clear all, which clears all of your expressions.

You can also type everything on the keypad from your keyboard.

Define Variables and Functions

You can define variables and functions and then reference them in subsequent calculations. The evaluation will appear on the right side of the expression line.

For example, try defining a variable by typing \(a=5\). You can then use a in any calculation. Or, define a function by typing \(f(x)=x^2+1\). You can then evaluate it by typing \(f(3)\), which will return \(10\). Click ans to reference the result of your previous calculation in a new expression.

Scientific calculator showing the function f(x)= x squared plus 1, with f(3) evaluated and returning a result of 10. Screenshot.

Understanding Your Results

When a result can be expressed as a fraction, a fraction icon fraction icon will appear next to the result. For example, \(1 + \frac{5}{8}\) displays as \(1.625\) by default. Click Fraction to display the result as \(\frac{13}{8}\) instead. Click Fraction again to return to the decimal form.

The calculator will automatically display very large or very small results in scientific notation. You can also enter numbers in scientific notation directly by typing them in the expression line.

Scientific calculator showing 1 + ⅝ evaluated to 13/8, with the fraction icon pressed. Screenshot.

Lists

You can make lists using square brackets \([ ]\). For example, you can type \([1,2,7,10]\) to make a four-element list with the values \(1, 2, 7,\) and \(10\). You can use lists anywhere in the calculator where you would enter a number.

Type an ellipsis (...) between elements to generate a list with evenly spaced elements. For example, typing \([1...10]\) will give you a list of all the integers between \(1\) and \(10\). If you type \([1,3...11]\), you’ll get a list of all six odd numbers between \(1\) and \(11\).

If you compute using a list, the calculator will run the computation on each element of the list. For example, \([1...5]^2\) will return a five-element list. You can also name a list as a variable and access individual elements using bracket notation. For example, if \(L=[1...5]^2\), then \(L[3]\) will return \(9\).

A list in square brackets containing 1, 2, 7, and 10, labeled as a 4 element list. Screenshot.

 

Complex Numbers

Computing with Complex Numbers

Complex numbers are written in the form \(a+bi\), where \(a\) is the real part and \(b\) is the imaginary part. To compute with complex numbers, open the Settings menu and then toggle on Complex Mode.

In complex mode, the calculator will display all angles in radians. You can add, subtract, multiply, and divide complex numbers in the expression line.

Functions for Complex Numbers

Function Try typing... This function plots or finds the...
real real\(\mathbf{(2+4i)}\) real part of a complex number.
imaginary imag\(\mathbf{(2+4i)}\) imaginary part of a complex number (multiple of \(i\)).
conjugate conj\(\mathbf{(2+4i)}\) complex conjugate by changing the sign of the imaginary part of a complex number. This is often used when dividing by complex numbers.
argument arg\(\mathbf{(2+4i)}\) angle inclined from the positive real axis to the line from the origin to the complex value. In Desmos, this angle is calculated in radians within the interval \((-\pi,\pi]\).
modulus, or absolute value \(\mathbf{|2+4i|}\) the distance between the origin and the complex value’s corresponding point.

 

Learn More

To learn more, reach out to us at support@desmos.com with any questions. As a start, here are a few articles that may be useful as you learn more about additional features: