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`Surface Area = pi( "a" + "b" ) sqrt( h_2 ^2+( "b" - "a" )^2) + 2*pi* "b" * h_1 + pi* "b" ^2`

Enter a value for all fields

The **Surface Area of a Bottle** calculator computes * A non-curved Bottle *the surface area (**A**) of a bottle. YouTube video instructions can be seen HERE. For the **Volume of a Bottle, CLICK HERE**. For the **Mass of the Contents of a Bottle, CLICK HERE**.

**INSTRUCTIONS:** Choose your preferred length units (e.g. centimeters or inches) and enter the following (see diagram):

- (
**a**) - neck radius at the top of the bottle - (
**h**) - the height of the tapered neck section_{2} - (
**b**) - the base section's radius - (
**h**) - the height of the bottle's base that is a constant diameter along it's length from the bottom base to the beginning of the taper._{1}

**Bottle Surface Area (A):** The calculator returns the area in square centimeters (cm^{2}). However, this can be automatically converted to many other area units (e.g. square inches or even acres) via the pull-down menu.

The formula used in this calculator is as follows:

`A = pi(a+b) sqrt(h_2^2+(b-a)^2) + 2*pi*b*h_1 + pi*b^2`

The surface area (**A**) includes several geometric shapes: the tapered neck, the cylindrical body and the circular bottom. You can see this in the three components of the formula:

- tapered neck (
**frustum of a cone**): `A = pi(a+b)sqrt(h_2^2 + (b-a)^2)` - cylindrical body (
**cylinder**): `A = 2pi*b*h_1` - circular bottom (
**circle**): `A=pi*b^2`

Geometrically, a bottle shaped object is the combination of right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h_{2}) in between and a cylinder of radius (b) and height (h_{1}). The surface area is the sum of the surface of the cone frustum, the cylinder and the circle of the bottom. Note: this leave no surface area for the opening at the top.