Pyramid Cutting Angles Calculator

Pyramid Angle Formula:

\[ \text{angle} = \arctan\left(\frac{\text{height}}{\text{base}/2}\right) \]

Angle (degrees):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Pyramid Angle Formula?

The pyramid angle formula calculates the angle of inclination for pyramid sides based on the height and base dimensions. This is essential for construction, woodworking, and pyramid design projects where precise cutting angles are required.

2. How Does the Calculator Work?

The calculator uses the pyramid angle formula:

\[ \text{angle} = \arctan\left(\frac{\text{height}}{\text{base}/2}\right) \]

Where:

\( \text{height} \) — Vertical height of the pyramid (m)
\( \text{base} \) — Length of the base side (m)
\( \arctan \) — Inverse tangent function

Explanation: The formula calculates the angle between the pyramid's side and its base by finding the arctangent of the ratio between the height and half of the base length.

3. Importance of Pyramid Angle Calculation

Details: Accurate angle calculation is crucial for constructing pyramids with proper structural integrity, ensuring pieces fit together correctly, and achieving the desired aesthetic appearance in architectural and craft projects.

4. Using the Calculator

Tips: Enter the pyramid height and base length in meters. Both values must be positive numbers. The calculator will compute the angle in degrees between the pyramid side and base.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for different pyramid types?
A: This formula works for regular square pyramids. For pyramids with different base shapes, additional calculations may be needed.

Q2: What units should I use for measurements?
A: The calculator uses meters, but you can use any unit as long as you're consistent (both height and base in the same units).

Q3: How accurate is the calculated angle?
A: The calculation is mathematically precise based on the input values. For practical applications, consider adding a small tolerance for cutting and construction.

Q4: Can I calculate base or height from a known angle?
A: Yes, you can rearrange the formula: height = (base/2) × tan(angle) or base = 2 × height / tan(angle).

Q5: Does this work for truncated pyramids?
A: No, this formula is for complete pyramids. Truncated pyramids (frustums) require different calculations.