Calculate instantly online! Your math assistant to calculate the surface area of a sphere easily.
Sphere Surface Calculator
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The following online calculator is an online tool to calculate the surface area of a sphere, based on the radius. The application calculates the area of the sphere using the formula Surface = 4 × π × radius². It allows you to calculate the spherical surface of any element, whether small or large.
Additionally, as an option, you can calculate the surface area of the sphere by also entering the diameter or its circumference.
How does the sphere surface calculator work?
To calculate the outer layer of a sphere follow these steps:
- Enter the value of the radius (r):
- Enter the radius of the sphere in the indicated field and select the unit of dimension. Optionally, you can use the diameter and circumference to calculate the area of the sphere.
- Calculate the surface area of the sphere:
- The sphere area calculator will automatically perform the calculation and display the surface area of the sphere according to the selected unit.
We remind you that the formulas to calculate the spherical surface vary depending on the distance to be used:
- To calculate the surface area of a sphere with the radius, the formula is: Surface = 4 × π × radius²
- To calculate the surface area of a sphere with the diameter, the formula is: Surface = π × diameter²
- To calculate the surface area of a sphere with the circumference, the formula is: Surface = Circumference² / π
🟧 Note: The formula to calculate the envelope of a sphere is universal, and remember that the Number pi = π is approximately 3.1416
Example of calculating the surface area of a sphere:
- If we have a sphere with a radius of 5 cm and we want to know the area of the spherical shell, we would apply the following calculation: Surface = 4 × π × (5 cm)² ≈ 314.16 cm².
- If we know the diameter of a sphere, for example, 10 cm, we apply the formula to calculate the spherical surface of Surface = π × diameter², and we get a result of 314.16 cm².
What units can you use in the calculator to calculate the surface area of a sphere?
The calculator to obtain the surface area of a sphere allows you to enter values in the following units:
- Millimeters (mm)
- Centimeters (cm)
- Meters (m)
- Kilometers (km)
- Inches (in)
- Feet (ft)
- Yards (yd)
- Miles (mi)
You can calculate the surface area for any sphere, as long as the input values are positive. Additionally, you can change the input and output units to adapt them to the metric or imperial system.
🟧 Note: If you have any questions about this online calculator to calculate the surface area of spheres, feel free to contact us from the contact section in the footer.
Frequently asked questions about the surface area of a sphere – FAQ
What is the surface area of a sphere?
The surface area of a sphere is the total area of the outer layer of a sphere, similar to the “skin” of a ball. It is a two-dimensional measure.
How is the surface area of a sphere calculated?
The formula to calculate the surface area of a sphere is: Surface = 4 × π × radius², where the Number pi = π is approximately 3.1416. For example, if I have a sphere with a radius of 15 cm, the calculation would be = 4 × π × 15² equivalent to 2827.43 cm².
What does the term πpi (pi) mean in the sphere formula?
The symbol π (pi) is a mathematical constant that is approximately 3.1416. It represents the ratio between the circumference of a circle and its diameter.
What units are used to measure the surface area of a sphere?
The units of area are expressed in square units, such as square meters (m²), square centimeters (cm²), etc.
What information do I need to calculate the surface area of a sphere?
You only need to know the radius of the sphere. If you don’t have the radius but know the diameter or the circumference, the spherical area can also be calculated.
What is the difference between the area of a sphere and its volume?
The area refers to the external surface of the sphere (what you could “paint”). And the volume measures how much space is inside the sphere.
If I double the radius, how does the surface area of the sphere change?
If you double the radius, the surface area of the sphere increases four times. This is because the radius is squared in the formula.
Is the formula for the surface area of a sphere valid for any sphere?
Yes, as long as the sphere is perfect and has a regular geometric shape. It does not apply to irregular spherical objects.
What is the surface area of a sphere used for?
It is used in many areas, such as engineering, design, astronomy (for planets or stars), and to solve practical problems like calculating the amount of material needed to cover a sphere.
How is the surface area of a hemisphere calculated?
To calculate the surface area of a hemisphere you need to add two areas: The curved surface of the hemisphere whose formula is Surface = 2πr², and the flat base of the hemisphere whose formula is Surface = πr². Then we just have to add both values to get the total area of the hemisphere.
What if I don’t know the radius or the diameter, but I do know the volume of the sphere?
You can calculate the radius from the volume using the formula Volume = (4/3) × π × radius³. Then, use the radius to calculate the surface area.
Is the surface area of a sphere the same as that of a hemisphere?
No. The surface area of a hemisphere is half of the sphere, but you must add the area of the base circle if necessary.
