Height of a Square Pyramid Calculator

Welcome to the height of a square pyramid calculator! This calculator, which focuses on determining the height (H) of a right square pyramid, is part of our calculator series that deals with different types of pyramids. In this calculator, you will learn:

• how to find the height of a square pyramid,
• the pyramid dimensions you need to calculate H, and
• the different formulas to find H.

Keep on reading to start learning 🙂.

The height of a square pyramid, also called altitude, is the perpendicular distance between its base and its vertex. When asked how tall a pyramid is, the pyramid's height is what we find.

Since pyramids are solid figures, they have volume. And we can use that to determine the height of a pyramid.

It is easy to determine the height of a square pyramid when you know its volume and base area. You simply have to multiply the volume by three and divide everything by the base area, as shown in the formula below:

H = 3 * V / A_b

Where:

• H is the height of the pyramid;
• V is the volume of the pyramid; and
• A_b is the pyramid's base area.

Since the base area is equal to the square of the base edge, A_b = a², we can also express the equation above in terms of V and a like this:

H = 3 * V / a²

As you may have noticed, to find the height of the right pyramid, we would need the base edge, a, and a parameter that indicates that the pyramid is a solid figure. Those parameters include the pyramid's volume (as described above), slant height (s), and lateral edge (d). You can learn more about these dimensions in our right square pyramid calculator.

If you know a right square pyramid's base edge length and slant height, you can use this formula to find H:

H = √(s² - (a / 2)²)

On the other hand, if you can measure its lateral edge, this is what you can use:

H = √(d² - a² / 2)

The formulas above are pretty much what you need to find H in most situations. However, sometimes we're not given the values for such parameters. So here are the formulas for the lateral face area (A_f), total lateral area (A_l), and total surface area (A) that you can use to extract the value of the slant height, given the base edge, a:

• A_f = a * s / 2

• A_l = 2 * a * s

• A = a² + 2 * a * s

This height of the square pyramid calculator is very straightforward to use.

1. The first step is to select which pair of measurements you want to use to find H.
2. Then, enter those measurements' values. Instantly, you'll get your pyramid's height.
3. If you want to see every measurement and play around with the calculator, select any custom pairs in the options.

Now that you know how to find the height of a square pyramid, here is a list of our other pyramid-related calculators that you can explore if you're craving for more:

• Right rectangular pyramid calculator;
• Pyramid volume calculator;
• Square pyramid calculator;
• Pyramid angle calculator;
• Square pyramid volume calculator;
• Right square pyramid calc;
• Surface area of a square pyramid calculator;
• Rectangular pyramid volume calculator; and
• Surface area of a rectangular pyramid calculator.

The Louvre Pyramid is about 21.6 meters (70.9 ft) high. We can also find its height using these steps:

1. First, measure its base edge length to get around 35.0 m (114.8 ft).
2. Try to measure its slant height where we'll obtain 27.8 m (91.2 ft).
3. Use the Pythagorean Theorem, H = √(s² - (a / 2)²) = √(27.8² - (35 / 2)²) = 21.6 m

Given the volume and base edge of a pyramid, you can follow these steps to calculate the pyramid height:

1. First, square the base edge to find the base area.
2. Then, divide the known volume by the base area.
3. Finally, multiply the obtained quotient by 3 to get the pyramid height.