A tangential quadrilateral is a special kind of four-sided shape that stands out because it has an amazing geometric feature: a circle can be drawn inside it that touches all four of its sides. This circle is called an incircle, and it gently "kisses" each side at exactly one point. These points are called points of tangency.
Not every quadrilateral can have this property. For a quadrilateral to be tangential, it must follow a specific rule: the sum of the lengths of one pair of opposite sides must be equal to the sum of the lengths of the other pair. Mathematically, this means:
a + c = b + d
Here, a, b, c, and d represent the lengths of the four sides. If this condition is not met, the sides cannot all touch the same circle from the inside, and the shape is not tangential.
This property creates a perfect balance within the shape, which is why tangential quadrilaterals are often considered elegant and symmetrical in geometry. Some well-known types of tangential quadrilaterals include the kite and rhombus, but a tangential quadrilateral doesn't need to be symmetrical — it just needs to satisfy the side-sum rule.
Tangential quadrilaterals are commonly studied in math because they combine both linear and circular geometry. They also appear in real-life applications like architectural design, tiling patterns, and even coin shapes where balanced edges are important.
Understanding this type of shape helps deepen your knowledge of how geometry works and opens the door to more advanced problem-solving — especially when it comes to calculating area, perimeter, or constructing shapes that have an incircle.
The Tangential Quadrilateral Calculator is a handy tool that helps you quickly find missing values in a tangential quadrilateral without needing to do complex math by hand. Whether you’re a student, teacher, designer, or simply curious about geometry, this calculator saves time and effort by doing the calculations for you.
With just a few inputs, the calculator can:
This is especially useful because tangential quadrilaterals follow a specific rule — the sum of opposite sides must be equal — and this calculator applies that rule instantly to find the missing values for you.
All you need to do is:
You can also choose how many decimal places you want the answers rounded to, giving you flexibility for homework, construction plans, or technical projects.
This calculator takes the guesswork out of the equation, helping you better understand and work with tangential quadrilaterals — faster and easier!
To use the Tangential Quadrilateral Calculator correctly, it’s helpful to understand what each input field means. Below is a simple explanation of each field and its purpose:
These are the four sides of the tangential quadrilateral. You can label them in any order around the shape, but the important thing is that the sum of opposite sides must be equal:
a + c = b + d
You need to enter any three out of the four sides. The calculator will automatically compute the missing side using the rule above.
This is the radius of the incircle, the circle that touches all four sides of the quadrilateral from the inside. If you enter the radius and three sides, the calculator can find the area for you.
This is the total area of the quadrilateral. If you know the area and the side lengths, the calculator can compute the radius of the incircle. The formula it uses is:
A = r × (a + c)
You only need to enter either the radius or the area — not both. If you enter both, the calculator will ask you to choose just one.
Once the required values are entered, just hit the “Calculate” button, and the rest will be filled in automatically!
To get accurate results from the Tangential Quadrilateral Calculator, you need to enter a specific combination of values. Don’t worry — it’s simple! Just follow the steps below:
You must enter the lengths of any three out of the four sides of the quadrilateral. The calculator will use the special rule of tangential quadrilaterals to automatically compute the fourth side:
a + c = b + d
This means if you know sides a, b, and c, the calculator will find side d for you — and so on.
Next, you need to enter one more value:
You should enter only one of these. If you enter both, the calculator will not work and will show an alert message asking you to choose just one.
Let’s say you enter:
The calculator will:
Simple, fast, and helpful — just make sure to follow these two basic steps to get started!
Using the Tangential Quadrilateral Calculator is quick and easy. Just follow these simple steps to get your results:
Start by entering:
Leave the fourth side blank — the calculator will figure it out for you automatically.
Choose how many decimal places you want the results to be rounded to. You can select from 0 to 15 decimal places using the dropdown labeled "Round to". By default, the calculator uses 3 decimal places.
After entering the required values and selecting the rounding option, click the “Calculate” button. The calculator will instantly:
To clear all fields and start over, simply click the “Delete” button. This will reset all input and output fields so you can try new values.
That’s it! You’re now ready to explore and calculate with confidence.
Once you click the “Calculate” button, the calculator quickly processes your input and displays the missing information. Here’s what you’ll see and what it means:
If you entered three sides, the calculator automatically fills in the missing fourth side using the special rule for tangential quadrilaterals:
a + c = b + d
This ensures that the shape is mathematically correct and can have an incircle.
Depending on what you provided:
Only one of these two values needs to be entered — the calculator will figure out the other one for you.
Once all four side lengths are known (either entered by you or calculated), the calculator adds them together and shows the total perimeter of the quadrilateral:
Perimeter = a + b + c + d
This is useful if you're planning to build, draw, or analyze the shape for design or academic purposes.
Each result is shown using the decimal precision you selected, so the numbers are easy to read and match your preference.
When working with measurements, it’s often helpful to round your results to a certain number of decimal places — especially if you're using the values for construction, schoolwork, or quick estimation.
This calculator gives you the flexibility to choose how precise your results should be. Just use the "Round to" dropdown menu located near the bottom of the calculator form.
Let’s say the exact result for the radius is 3.1415926535:
3.143.14159This feature is useful when you want results that are either quick and clean or highly precise, depending on your task.
Simply set your desired precision before clicking the “Calculate” button, and the calculator will apply your choice to all outputs automatically.
To get the best experience with the Tangential Quadrilateral Calculator, keep these helpful tips and warnings in mind. They’ll help you avoid errors and understand how to use the tool correctly.
If the calculator shows an alert or doesn’t give a result, it’s usually because of one of these issues:
If you’re unsure what went wrong, click the “Delete” button to clear the form and start fresh.
Remember: the calculator is built to handle valid tangential quadrilaterals only. If the values you enter do not satisfy the rule a + c = b + d, the results may not make sense.
When in doubt, double-check your inputs or try a different combination. With a bit of practice, you’ll find the calculator fast and easy to use!
A tangential quadrilateral is a four-sided shape where all sides can touch an inscribed circle (called the incircle). This happens only if the sum of one pair of opposite sides equals the sum of the other pair: a + c = b + d.
No. You can label the sides in any order, as long as you enter exactly three sides. The calculator will use the side-sum rule to find the missing one.
No. The calculator is designed to compute one side based on the other three. If you enter all four, it won’t work properly and may show an error.
No. You should enter only one of them. If you enter both, the calculator will display an error. Choose either the radius to find the area, or the area to find the radius.
The calculator will not run and will show an alert message. Make sure you enter:
Yes! Use the "Round to" dropdown to select the number of decimal places you want in your results — from 0 up to 15 decimal places.
Yes, the calculator uses precise geometric formulas designed specifically for tangential quadrilaterals. Just make sure your inputs follow the required rules.
Absolutely. The calculator is designed to work on various screen sizes, so you can use it on a desktop, laptop, tablet, or smartphone.
Click the “Delete” button to clear all fields and start fresh. If you still have trouble, double-check that you’ve entered the correct combination of values.