Here you can find pre-built calculation and design templates from all kinds of different disciplines and areas. You can use them as is or duplicate them into your own workspaces and make them your own!

Templates

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Calculation templates

Welcome to the Mathematics library, where you'll find loads of handy maths calculations and explanatory content for you to browse and use.

They're great for using as a base for a project. If you'd like to make any calc your own, just duplicate it into your workspace, and it's yours!

Square, Cube, Square Root and Cubic Root Calculator

Maths Calculations

Free-To-Use Maths Calculations: Get Accurate and Fast Results with CalcTree. Solve Complex Math Problems in Seconds! Start using now!

Welcome to our online square, square root, cube, and cubic root calculator! Whether you're a student tackling math problems or a professional working on complex equations, our calculator is here to assist you. It's a convenient tool designed to provide you with accurate and quick results.

The square calculator online function allows you to find the square of a number, which is obtained by multiplying the number by itself. For example, if you input 5, the calculator will display the result as 25, since 5 times 5 equals 25.

Our square root calculator online function is another important tool. The square root is the inverse operation of squaring a number. For instance, if you enter 25, the calculator will provide the square root as 5.

Want to solve cubic equation online too? Our calculator has got you covered. The cube function allows you to find the cube of a number, which is obtained by multiplying the number by itself twice. For instance, if you input 3, the calculator will display the result as 27, since 3 times 3 times 3 equals 27.

Lastly, our cubic root calculator online function can assist you. The cubic root is the inverse operation of cubing a number. For example, if you input 27, the calculator will provide the cubic root as 3.

If you liked this, check out our other articles and resources!

Calculate squares, cubes, square roots, and cubic roots on CalcTree. Free-to-use engineering calculator. Simplify your calculations now.

Square Root Calculator | Cubic Root Calculator

Welcome to our Pythagoras calculator! This page will allow you to find the missing side of a triangle, specifically the hypotenuse. 

Pythagorean theorem fundamental geometric relationship between three sides of a right angled triangle. It states that the area of the square whose side is the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b). Given this relationship, we can derive an equation relating the lengths of the sides a, b and the hypotenuse c:

Need a side other than the hypothenuse? Check this page out:

Determine the Length Of a Side

Pythagorean Theorem Calculator 

Solve with ease on CalcTree. Free-to-Use online pythagorean theorem calculator. Calculate side lengths and hypotenuse. Get Instant Results!

Pythagorean Theorem Calculator Online

This triangle calculator page provides a simple calculation to determine the angles in a right-angled triangle using 

. It also acts as a hypotenuse calculator. 

Triangle Angle Calculator

Need to calculate triangle angles? Look no further than CalcTree. Free-To-Use Triangle Angle Calculation tool. Try it now. No signup is required!

Triangle Angle Calculator | Find Angle of Triangle | Triangle calculator

This page provides some insight into equilateral triangles! Not only is it an equilateral triangle height calculator, it is also an area of equilateral triangle calculator, and can too find the perimeter of an equilateral triangle! 

The perimeter of an equilateral triangle is given by: 

Equilateral Triangle Calculator

Instantly compute equilateral triangle properties on CalcTree. Free-to-use online equilateral triangle calculator.  Calculate now!

Equilateral Triangle Calculator 

This right angled triangle calculator provides some functions to find the length of the hypotenuse and the area of the triangle!

A right-angled triangle is a triangle where one of the angles is a right angle (90 degrees). The hypotenuse is the longest side of a right-angled triangle, and it is always opposite to the right angle. The other two sides are called the legs, often referred to as base and height.

To calculate the length of the hypotenuse, we can use the Pythagorean theorem. Check out our page on 

 for an in-depth explanation. It's important to note that the Pythagorean theorem only applies to right-angled triangles.

Check out this page if you are after the 

length of a side that is not the hypotenuse

Right Triangle Calculator

Effortlessly solve right triangle problems on CalcTree.  Free-to-use online right triangle calculator. Empower your trigonometric calculations today!


This page provides some insight into Heron's Formula and allows you to find the area of triangle using Heron's Formula!

Heron’s formula is credited to Heron of Alexandria (c. 62 CE) and used for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides:

Heron's Formula Calculator

Quickly find area using Heron's formula on CalcTree. Free-to-use online heron's formula calculator. Simplify complex area calculations now!

Find The Area of Triangle Using Heron's Formula Calculator

Wanting to calculate arc length? Use our arc length of curve calculator to do so, given the radius and the angle formed by the arc. 

Arc length is a measure of the distance along the curved line of a circle and is an important 

The equation for the area of the sector it creates is:

Where θ is the central angle in radians and r is the radius of the circle.

Calculate Arc Length and Sector Area

Calculate area and arc length of a circle sector on CalcTree. Free-to-use online circle arc calculator. Calculate now!

Circle Arc Length Calculator | Circle arc calculator

Calculate Arc Length

Welcome to our circle dimension calculator! This page can be used as a circle area calculator, a circumference of a circle calculator, and a circle diameter calculator! We will use the radius of a circle, "r", to find these parameters. 

This page also can work the other way around as a circle radius calculator, if the area or circumference of the circle is provided. 

The following calculations are a great way to get a better understanding of circles and their properties. Let's begin!

Diameter refers to a straight line that reaches from one point on the edge of a round shape or object, through its centre, to a point on the opposite edge.

Similar to the term 'perimeter' of polygons, circumference is the linear distance of a circle's edge. However, the term perimeter is not used for circles. 


Circle Dimension Calculator

Calculate various dimensions of a circle - radius, diameter, circumference, and area on CalcTree. Free-to-use Circle Dimension Calculator. Try it now!

Circle Area Calculator | Circumference of A Circle Calculator

After a cube volume calculator? What about one that doubles as a cube surface area calculator? 

A cube is a three-dimensional solid figure with 6 flat faces, 8 corners and 12 edges. We will use the side length, "s", of the cube in this volume and surface area of a cube calculator.

To find the volume of a cube, you must find the product of its three dimensions, which are all the same size and shape. To calculate the volume, you multiply the length of one side of the cube by itself three times. 

So, for a cube with a side length of "s", the formula for the volume is: 

The volume of a cube calculator above will do this for you!

Cube Surface Area & Volume Calculator

Free-To-Use cube surface area & volume calculator helps you to quickly find the surface area, volume and diagonal of a cube. Try now!

Cube Area Calculator | Cube Volume Calculator |

Welcome to our dodecahedron calculator! A dodecahedron is a three-dimensional solid figure with 12 flat faces. It is one of the five Platonic solids, which are regular polyhedra. 

principles to find the surface area and volume of a dodecahedron. 

To do this, we will use the length of each of the dodecahedron's edges to calculate the area of each face. 

Once the area of each face is known, we can calculate the total surface area and volume of the dodecahedron.

Dodecahedron: Surface Area & Volume

Calculate the surface area and volume of a dodecahedron on CalcTree. Free-to-use Dodecahedron Calculator. Calculate now!

Dodecahedron Calculator - Determine Surface Area & Volume

Wanting a surface area of a cylinder calculator? Or after a volume of cylinder calculator? What about one that does so in SI, metric and imperial units! This page does it all!

A cylinder is a three-dimensional object with two flat circular faces joined by a singular curved surface.

In this volume and surface area of cylinder calculator, we will use basic 

Volume & Surface Area of Cylinder Calculator

Calculate the surface area and volume of a cylinder on CalcTree. Free-to-use Cylinder Capacity Calculator. Get started today!

volume of cylinder calculator | surface area of cylinder calculator

On this page, we're looking at spheres! Not only is this a sphere volume calculator, it will also calculate sphere surface area, double trouble! 

A sphere is a geometrical object, a three-dimensional counterpart of a two-dimensional circle. It is defined as the set of points in three-dimensional space equidistant from a given point, known as the sphere's centre, with a radius denoted by 'r.' 

The sphere surface area calculator and sphere volume calculator will use these basic geometry principles in their determination.

Finding the volume of a sphere and calculating the surface area is as simple as using the below equations.

Let's find the surface area of a sphere of radius 7cm! 

Calculate Sphere Surface Area And Volume

Easily calculate sphere surface area And volume online on CalcTree. Free-To-Use sphere surface area calculator. Get Results Quickly














Sphere Surface Area Calculator | Sphere Volume Calculator 

In our everyday lives, we use the decimal number system known as base 10. This is an example of a 

. Computer science and engineering use other systems, such as binary and hexadecimal numbers, for various purposes. 

that uses only two symbols, 0 and 1, to represent numbers. Binary is used in electronic computer systems because they can be effectively mapped onto real electronic 'switches', which form the bases for modern computation.  

Hexadecimal is a base-16 numerical system 

characters A to F to represent the values 10-15

. Hexadecimal is used to store large numbers with fewer characters than binary and decimal, making it desirable in particular computational processes. 

Understanding how to convert between these different number systems is 

fundamental to electronic and software design

 into binary equivalents. Since the calculator uses a 

highest hexadecimal value that can be inputted is 3FF

So how do we convert between the different systems?

To understand how decimal, binary and hexadecimal values it is pivotal to understand the underlying principles behind their notation. 

Take the decimal system, for example, specifically the number 

 If we break this down into its powers of 10, we can observe each digit as a weighted value of a 10th power. 

We can perform this same step with each digit in a binary number, as each digit represents a power of 2. If we take a binary number, say 

, we can break it down into its constituent parts and better understand how binary numbers function. 

As is the case with decimal and binary, this base-16 number system essentially entails that each digit or character corresponds with a power of 16. If we take a hexadecimal number, say 

, we can break it down again into a set of constituent components. 

Table (2)

Converting from hexadecimal to binary can be achieved using the above table. However, for larger numbers, this proves more difficult, and thus we will highlight a simple method for achieving conversion. 

This method will involve converting from hexadecimal to decimal, then from decimal to binary. Let us use an example and explain the process simultaneously. Let's take the hexadecimal number 

We will continually divide the decimal number by two until we reach 0, using the remainder to construct the binary number with the first remainder as the least significant bit and the last remainder as the most significant bit. 

Now we have our equivalent binary number: 

The calculator at the top of this page is designed to convert 

To convert a decimal value that requires less than 10 bits (less than 512), you can find the last non-zero bit when reading the binary representation vertically from "Remainder_b1" to "Remainder_b10." This last non-zero bit will be the leading 1 in the binary representation.

It's important to note that the binary numbers 01001 and 1001 actually represent the same unsigned binary value. The leading 0 in the former case is discarded during the conversion process.

, you can accurately convert decimal values to their binary equivalents!

Here's a detailed breakdown of how this works (control the hex input from the top of the page).

In this article, we have covered the fundamental principles behind decimal (base 10), binary (base 2) and hexadecimal (base 16) positional number systems. 

We highlighted how to convert from binary and hexadecimal to a decimal number as well as conversion from a hexadecimal number to a binary number. 

Developing a concrete understanding of these number systems as well as how they relate to each other is a foundational building block for building and developing modern digital systems. 

Hexadecimal to Binary Converter

Effortlessly convert decimal, binary & hexadecimal numbers using CalcTree's Free-to-use hexadecimal to binary converter. Try it now!

Hexadecimal to Binary Converter - CalcTree

Aside from 1, 2 and 3, all of the prime numbers can be found to be of the forms:

 This does not mean that every value these equations produce is a prime number. If a prime number exists, it will fit into either of these two equations. 

If we take the values of n from 1 to 10, we can find the first 18 prime numbers: 

Table (1)

As mentioned, a few numbers: 25, 35, 49, and 55 are not primes. The most bulletproof method of measuring the primality of a number involves dividing the given number by every integer until the value itself. If the result is not a fraction or is a whole number, it will have a common factor and thus not be a prime. 

15/2

15/3

We can stop here, as 5 is a whole number. So 15 is not a prime number, as 5 is a common factor.

All results are fractions, therefore, 7 is a prime number, as it has no common factors besides 1. 

This prime is also shown in the table above, as each is 6n+1 or 6n-1. 

Prime numbers are crucial in number theory because of the 

: every natural number greater than 1 can be written uniquely as a product of primes (up to the order of multiplication). In other words, primes 

 the building blocks of all other natural numbers.

Prime numbers have diverse cryptography, computer science, and number theory applications. They are crucial for encryption algorithms like RSA, efficient data structures such as hash tables, and prime factorization algorithms. Their significance in these fields makes prime numbers indispensable in modern technology and 

Prime Number Checker

Check importance of prime number with our free-to-use prime number checker. Enhance your math skills at CalcTree. Try now!

Prime Number Checker - CalcTree

This calculator finds the probability of an event occurring a certain number of times (

 in a fixed interval of time or space when the mean number of events

 is known. This type of probability distribution is known as a Poisson distribution.

The Poisson distribution is a discrete probability distribution that describes the probability of an event occurring a certain number of times (

) in a fixed interval of time or space when the mean number of events (

) is known. It applies to problems in which random events occur independently of each other at a known average rate. 

A Poisson distribution can be represented visually as a graph of the 

. A probability mass function is a function that describes a discrete probability distribution. 

The most probable number of events is represented by the peak of the distribution, called the 

 is low, then the distribution is strongly rightly skewed. As 

 increases, the distribution looks more balanced. In fact as  

, Poisson distribution tends to a normal distribution. 

Poisson Distribution Calculator

The Poisson distribution is a discrete probability distribution that gives the probability of an event happening a certain number of times.

This tool calculates the harmonic mean, a type of average that is particularly useful when dealing with rates or ratios and in handling datasets with extreme values.

The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of a dataset. It is especially relevant when dealing with rates or ratios and in handling datasets with extreme values. 

Check out our full library of CalcTree templates 

Harmonic Mean Calculator

This tool calculates the harmonic mean, a type of average that is particularly useful when dealing with rates or ratios.

This calculator checks the alignment and geometry of circular curves, which is used in fields such as civil engineering, construction and surveying. It provides a visual of a curve based on the input parameters: radius of the circle, chord length and number of points. 

For the set out curve to be valid, this condition must be satisfied:

Set out curve using Tangential Angles Method:

matplotImage

The Tangential Angles Method, also referred to as the Rankine Method, uses a known value (chord length) and desired value (radius) to set out circular curves. 

Here is all the parameter symbols you need to know.

Set out curve using the Tangential Angles Method

Follow these steps to successfully set out your curve:

Tangential Angle Method for setting out circular curves

This calculator checks the alignment and geometry of circular curves, which is used in fields such as civil engineering, construction and surveying

 harmonic number, which is the sum of the reciprocals of the positive integers up to integer 

 is non-integer, the calculator computes the approximate harmonic number by using the digamma function and the Euler–Mascheroni constant.

The harmonic series approximates the natural logarithm plus the Euler-Mascheroni constant, that is:

This approximation becomes more accurate as 

 becomes larger. Because the harmonic series approximates the natural logarithm, it is a divergent series which means it grows infinitely.

The harmonic number is calculated in two different ways for integer and non-integer values of 

This calculator is particularly useful in scenarios such as:

Harmonic Number Calculator

This calculator computes the harmonic number, which is the sum of the reciprocals of the positive integers up to integer.

This calculator provides varies methods to compute the slope (also known as gradient). The methods are the slope-intercept form, point-slope form, slope of a right-angle triangle, and the Euler line form. 

Various methods for calculating the slope/gradient are provided in the toggles below.

Slope and gradient are dimensionless measures of the steepness of a line. They are calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, this is given by:

The terms slope and gradient are often used interchangeably, though gradient is sometimes distinguished from slope as being a vector quantity (while slope is a scalar).  

The importance of slope and gradient is vast and spans multiple fields:

In summary, slope and gradient are fundamental concepts in mathematics and science, providing a measure of change and playing a crucial role in understanding and interpreting phenomena in various fields.

Slope and Gradient Calculator

This calculator provides varies methods to compute the slope (also known as gradient). The methods are the slope-intercept form, point-slope form etc

This calculator converts inputs as polar coordinates to cartesian coordinates (and vice versa). A degree to radian converter (and vice versa) is also provided.

Polar and cartesian coordinates can be used to describe location, orientation or direction in a two-dimensional space at any time.

The polar coordinate system describes the location of a point in a 2D plane by defining a fixed point away from the origin, called the pole, and an angle moving counter-clockwise from the positive x-axis. A polar coordinate is expressed as 

The cartesian coordinate system, however, describes the location of a point in a 2D plane using a pair of numbers called an ordered pair. The ordered pair is expressed as 

 is the distance away from the origin along the horizontal axis and 

 is the distance away from the origin along the vertical axis. Direction in the cartesian coordinate system is expressed as a positive or a negative sign.

Discover how to convert between the two coordinate systems in the toggles below.

Polar-Cartesian Coordinate Converter

This calculator converts inputs as polar coordinates to cartesian coordinates (and vice versa), and includes a degree to radian converter.

This calculator graphs a user-specified function on a cartesian plane. It also tabulates the x and y values in a specified range.

A function establishes that for each value of x, there is a corresponding value of y under an explicit rule or formula. We can say, by definition, that "y is a function of x". Mathematically this is written as: 

This calculator's inputs can be mathematically expressed as:

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