Surface Area and Volume Calculator

Volume Formulas:

\[ V_{rect} = L \times W \times H \] \[ V_{cyl} = \pi \times r^2 \times h \]

Select Shape:

Length:

units

Width:

units

Height:

units

Volume:

Surface Area:

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1. What is a Surface Area and Volume Calculator?

Definition: This calculator computes the volume and surface area of various geometric shapes including rectangular prisms and cylinders.

Purpose: It helps students, engineers, and professionals quickly determine the volume and surface area of common 3D shapes.

2. How Does the Calculator Work?

The calculator uses different formulas based on the selected shape:

Rectangular Prism:
\[ V = L \times W \times H \] \[ SA = 2(LW + LH + WH) \] Cylinder:
\[ V = \pi \times r^2 \times h \] \[ SA = 2\pi r(r + h) \]

Where:

\( V \) — Volume (cubic units)
\( SA \) — Surface Area (square units)
\( L \) — Length
\( W \) — Width
\( H \) — Height
\( r \) — Radius
\( h \) — Height (for cylinder)

3. Importance of Volume and Surface Area Calculations

Details: These calculations are fundamental in engineering, construction, manufacturing, and many scientific applications for material estimation, capacity planning, and design.

4. Using the Calculator

Tips: Select the shape, then enter the required dimensions. All values must be positive numbers. The calculator will compute both volume and surface area.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: You can use any consistent unit (inches, feet, meters, etc.), just be sure all measurements are in the same unit.

Q2: Why is surface area important?
A: Surface area is crucial for material requirements (like paint or coating), heat transfer calculations, and packaging design.

Q3: Can I calculate other shapes?
A: Currently this calculator supports rectangular prisms and cylinders. More shapes may be added in future updates.

Q4: How precise are the calculations?
A: Results are precise to 3 decimal places. For π we use PHP's built-in pi() function which provides sufficient precision.

Q5: What if I get zero or negative results?
A: The calculator requires all dimensions to be positive numbers. Zero or negative values will not be processed.