Tank Bottom Surface Area Formula for Cathodic Protection

Tank bottom surface area calculations are commonly used when estimating CP current demand for aboveground storage tank bottoms. The bottom is usually treated as a circle for basic study calculations.

The calculation is straightforward, but it depends on whether the tank diameter or radius is provided.

Formula

A = π x r2

Symbol Meaning Common Unit
A Tank bottom area ft2
π Pi 3.1416
r Tank radius feet

Diameter to Radius

Tank size is often given as diameter. The radius is one-half of the diameter.

r = Diameter / 2

Worked Example 1: 60-Foot Diameter Tank

A tank has a 60-foot diameter. Estimate the tank bottom surface area.

r = 60 / 2

r = 30 ft

A = π x r2

A = 3.1416 x 30 x 30

A = 2,827 ft2

The estimated tank bottom area is approximately 2,827 ft2.

Worked Example 2: 100-Foot Diameter Tank

A tank has a 100-foot diameter. Estimate the tank bottom surface area.

r = 100 / 2

r = 50 ft

A = π x r2

A = 3.1416 x 50 x 50

A = 7,854 ft2

The estimated tank bottom area is approximately 7,854 ft2. This area may then be used with a current density or current requirement assumption.

Worked Example 3: Area to Current Requirement

A tank bottom has an estimated area of 7,854 ft2. A current density of 1 mA/ft2 is assumed. Estimate the current requirement.

I = A x D

I = 7,854 x 1

I = 7,854 mA

I = 7.854 amps

The estimated current requirement is approximately 7.9 amps. Actual tank-bottom CP performance depends on current distribution, tank pad conditions, anode layout, and reference cell reliability.

CP Interpretation Notes

  • Tank bottom area is an input to current demand calculations.
  • Diameter must be divided by two before using the circle area formula.
  • Actual CP performance depends on under-tank electrolyte and current distribution.
  • Fixed reference cells only represent their installed locations.
  • Area calculations do not prove compliance with CP criteria.

Common Mistakes

Using Diameter as Radius

If the tank diameter is used directly as the radius, the calculated area becomes much too large.

Ignoring Tank Pad Conditions

Sand pad condition, moisture, liners, and shielding can affect whether CP current reaches the tank bottom.

Overstating Cell Coverage

A fixed reference cell does not prove the entire tank bottom is protected.

Practice Problems

  1. A tank has an 80-foot diameter. What is the approximate bottom area?
  2. A tank has a 120-foot diameter. What is the approximate bottom area?
  3. A tank bottom area is 5,000 ft2 and the assumed current density is 2 mA/ft2. What current is required?

Related Pages

Field Use Reminder

Tank bottom area calculations support current-demand estimates, but under-tank CP performance depends on current distribution, tank pad continuity, electrolyte conditions, anode layout, and the reliability of fixed reference cells.