Online Scientific Calculator Instruction Manual



Thanks for trying out the new Online Scientific Calculator

Alcula's scientific calculator is frequently updated with new functionalities. Please check the new features updates for information about recent changes., Also, keep in mind that it may have bugs. Always double-check your results. If you do find any problems, please help me fix them by reporting the details of the problem using the feedback link at the bottom of the calculator page.

What is it? And what does it do?

The Online Scientific Calculator is an online application for performing simple mathematical calculations. Based on the feedback I received for the first version it now includes many additional features.

The most important change is the history display. All operations that you perform during the session are saved and displayed on the top portion of the calculator, so that you can look back at the previous steps you made. You can go back to previous expressions to make corrections and all following expressions are updated automatically. The number of operations that are saved is only limited by the amount of memory of your computer.

The direct text input feature enables you to enter the expression directly in the input field (the blue-bordered field above the keyboard). You never need to use the mouse to click on the keys. You may still use the mouse if you want to, but typing directly is probably much quicker and more confortable for long sessions.

You can define your own functions. The new functions that you create can be included in any expression, or in other functions.

Requirements

The calculator should work with most recent web browsers that support flash applications. You will need a recent version of Flash Media Player. The program is rather large, so you will probably need a broadband internet connection. After you use it the first time, it should be cached by your browser and it will load much quicker.

Starting the calculator

To use the calculator, goto the Calculator page. From the calculator page shift-click on the help link at top of the page to display this help document on a new window.

How to enter an expression

After the calculator has finished loading, you can enter expressions either by left-clicking with your mouse on the on-screen keyboard buttons or by typing directly inside the input field.


Type your expression in the input field


When you have finished typing your expression, press 'Enter' to evaluate it.

If the expression is syntactically correct, it gets processed and displayed on the history window, along with the result.

Fraction vs. Decimal Results

The calculator attempts to perform the calculations using fractions, to preserve precision.

For example, if you enter an expression such as '5/2+10/3', this will generate two results, next to each other:

'5/2+10/3  =35/6  ≈5.833333333333333'.

This means that the accurate result of the expression is '35/6' which is approximately equal to '5.833333333333333'.

With both rational and approximated results displayed this way you can pick the result that best suits your need.

When the rational result is the same as the approximate result, only the rational result is displayed. Likewise, if a rational result is not available, the calculator will only show the approximate result.

A few more examples:

History scrollbar

All expressions that you enter, along with the results are displayed on the upper portion of the calculator window. Wnen there is more space available in the visible area, a scroll bar is displayed on the right side of the calculator. You move the scroll bar by left-clicking on it and moving your mouse up or down while holding down the left button.


Use the scrollbar to scroll through the results


Retrieving previous expressions

When the input field is selected (you can tell when the input line is selected because the border is blue), you can retrieve previous expressions by pressing the Up-arrow key on your keyboard.

By using the Up and Down-arrow keys you can browse through the history of all the expressions you entered, modify them and recalculate the results as new expressions.

This can be handy if you realized you have made a mistake and want to recalculate the result without re-typing the whole expression.

Note that modifying an expression this way does not replace the previous expression but creates a new expression that is added to the bottom of the history.

Reusing the results of previous expressions: The ans() function

As you have seen previously, the upper portion of the calculator window contains the history of the expressions you entered, along with their rational result and approximate decimal result.

The first number in each line, underlined, is the sequential number of each expression. You can use this number as parameter to the ans() function to retrieve the result of the corresponding expression. For example, if expression number 5 was 5/4+4/3+3/2+22 =313/12, you can enter an expression like ans(5)-10 to obtain the result 193/12.

You can also use your mouse to quickly retrieve an answer by clicking on the underlined sequence number of the expression. This will enter the ans function for you in the expression input field.


Sequence number of expressions


Editing the history

One of the most important features of the online scientific calculator is the history editor.

Suppose you have entered many expressions, all part of the same problem, when you realize that you mistyped a number in the first expression. Normally you would have to start from scratch and redo all your calculations. With this calculator you can change an expression that you previously entered. Here is how to do it:

  1. Left-click on the expression that you want to modify.
  2. Correct it.
  3. Press the 'Enter' key or click on the '=' key of the on-screen keyboard.

The expression that you modified is automatically corrected, and all other expressions that use its result are recalculated as well. The re-calculations are performed recursively.

A simple example: You want to calculate the diameter, circumference and area of a circle with diamater 15. After you have entered the diameter and the expressions to calculate radius, area and circumference, you realize that instead of entering 15 for the diameter, you accidentally entered 25.

You left-click on the wrong expression, in this case the number 25:


Mistake: typed 25 instead of 15


The blue border moves to the expression that you clicked. You can now modify the value, change it to 15, then press 'Enter'


Correct the mistake by clicking on it


After you pressed 'Enter', all results of the following expressions are updated automatically.


Then press enter


Deleting the input line: The C ans AC keys

Use the 'C' key on the virtual keyboard to delete the character behind the cursor on the input line or the last typed character.

The 'AC' button deletes the whole input line.

Resetting the calculator

To reset the calculator click on the 'reset' key on the virtual keyboard. When you attempt to perform a reset, a confirmation window appears. Click on 'ok' to complete the reset or on 'cancel' to abort the operation. When you reset the calculator all expressions in the expression history are deleted. THere is no way to retrieve the expression history after a reset.

Note that a reset of the calculator does not delete 'user functions', even if they were entered through the calculator being reset (see Defining User Functions below).

More information on using the virtual keyboard

The keyboard is useful for using the calculator using a pen from a mobile device or a tablet PC.

When using the keyboard, remember that the online scientific calculator is a 'formula calculator' versus an 'immediate execution calculator'. This means that you enter your expressions as you would write them on a piece of paper.

As an example, imagine you want to calculate the cosine of pi on a traditional pocket calculator: You would press the 'pi' button first, followed by the 'cosine' key. It doesn't work this way on this calculator. To calculate cos(pi), you first press the cos button (or type 'cos(' on the input field), then you press the 'pi' button, then press the ')' key to close the parenthesis, and finally press the '=' button to make the calculation.

This method of input allows you to use parenthesis to specify the order of operations. For more information on formula calculator and calculator input modes, see this wikipedia article: Calculator input methods.

About 'NaN' and 'Infinity'.

The calculator will return the value 'NaN' for operations that cannot be performed, for example the square root of a negative number.

The 'Infinity' value is returned for division by 0 and for values that are too large for the calculator to process, even though these values are not technically infinite.

Defining your own custom functions

The online calculator can save you a lot of time if you need to perform the same calculation many times for different values.

You can define a named function to use in your expressions.

Using Custom Functions in Expressions

Once you have defined a custom function, you can use it in expressions the same way as you use built-in functions. For example, if you have defined a function volume that calculates the volume of a cube ( volume(x,y,z)=x*y*x ), you can write an expression like volume(2,2,5)+volume(3,3,6) to sum the volumes of two cubes.

Use your new function in expressions


Replacing custom Functions

You can replace an existing custom function by redefining it with the same name. However, if the function is already in use, you will get an error if you attempt to change the number of parameters.

When you replace a function, all expressions that use that function and all expressions that use a function that is dependent on the one you replaced, are updated automatically.

Deleting Custom Functions

Custom functions can only deleted if they are not used by other functions or by other expressions.

To delete a custom function press the 'delete' button next to the function that you want to delete. The button is graded out if deletion is not possible.

Once you have used a custom function in an expression you will not be able to delete it until you reset the calculator (see Calculator Reset above).



Currently Supported operations

The Calculator supports the following operators and functions:

Basic Functions
FunctionSyntaxKeyExplanation
Addition <number>+<number> + The sum of two numbers.
Subtraction <number>-<number> - The subtraction two numbers.
Multiplication <number>*<number> X The multiplication of two numbers.
Division <number>/<number> / The division of two numbers is calculated left-to right.
Power <number>^<number> ^ Elevation of a number to the power of another.
Square root sqrt(<number>) sqrt The division of two or more numbers is calculated left-to right.
Constants
ConstantSyntaxKeyExplanation
e e e The constant e (≈2.71828182845905).
π pi pi The constant π (≈3.141592653589793).
Logarithms
FunctionSyntaxKeyExplanation
Natural logarithm ln(<number>) ln The natural logarithm of a number.
Common logarithm log(<number>) log The common logarithm (log10)of a number.
Trigonometric Functions
FunctionSyntaxKeyExplanation
Sine sin(<number>) sin The sine of a number in radians.
Cosine cos(<number>) cos The cosine of a number in radians.
Tangent tan(<number>) tan The tangent of a number in radians.
Inverse Sine asin(<number>) asin The inverse sine of a number.
Inverse Cosine acos(<number>) acos The inverse cosine of a number.
Inverse Tangent atan(<number>) atan The inverse tangent of a number.
Hyperbolic Sine sinh(<number>) sin The hyperbolic sine of a number in radians.
Hyperbolic cosine cosh(<number>) cosh The hyperbolic cosine of a number in radians.
Statistics
FunctionSyntaxKeyExplanation
random rand() rand Return a pseudo-random number between 0 and 1.
Factorial <number>! ! The factorial of a number. For non integer numbers, the factorial is calculated using the Stirling formula.
Permutations perm(<number>,<number>) perm The permutations of (n,r).
Combinations comb(<number>,<number>) comb The combinations of (n,k).
Other
FunctionSyntaxKeyExplanation
Absolute Value abs(<number>) abs The absolute value of a number.
Answer ans(<number>) ans The result of a previous expression.
Reset n/a reset Resets the calculator window.