Current Density for Cathodic Protection

Quick Definition

Current density is calculated as:

In symbols:

Where:

• J is current density.
• I is current.
• A is area.

Common units include:

• A/ft²
• mA/ft²
• A/m²
• mA/m²

The current and area units determine the current-density units.

When Current Density Is Used in CP Work

Current density may be used when:

• comparing current to a known or estimated surface area;
• estimating current per square foot or square meter;
• discussing total area versus exposed area;
• comparing current-density assumptions;
• supporting current-requirement discussions.

Current density is not the same as total current.

A small area with a given current has a higher current density than a large area with the same current.

This page does not tell you what current density to use for design. Design values require source support and engineering judgment.

Formula Reference

Variable and Unit Table

Use consistent units:

• amps divided by square feet gives A/ft²;
• milliamps divided by square feet gives mA/ft²;
• amps divided by square meters gives A/m²;
• milliamps divided by square meters gives mA/m².

Common Conversions

• 1 A = 1000 mA
• 1 mA = 0.001 A

How to Use the Formula

Use J = I ÷ A when current and area are known.

Before calculating, decide what area is being used:

• total surface area;
• exposed area;
• bare area;
• tank bottom area;
• pipeline outside surface area.

The answer depends on that area. If the area is only an estimate, the current density is also only an estimate.

Do not treat a current-density value as a universal requirement. This page explains the calculation, not a design standard.

Worked Example 1 — Current Density in A/ft²

A CP system applies 2 amps to an estimated exposed area of 100 ft². What is the current density?

Known values:

• I = 2 A
• A = 100 ft²
• J = ?

Use:

Substitute:

Calculate:

Answer: The current density is 0.02 A/ft².

Field meaning: This describes current per square foot for the area used in the calculation. It does not tell you whether the structure is protected.

Worked Example 2 — Current Density in mA/ft²

A current of 500 mA is applied to 25 ft² of estimated exposed area. What is the current density?

Known values:

• I = 500 mA
• A = 25 ft²
• J = ?

Use:

Substitute:

Calculate:

Answer: The current density is 20 mA/ft².

Field meaning: This calculation uses milliamps, so the answer is in milliamps per square foot.

Worked Example 3 — Solve for Current

A current density of 10 mA/ft² is used for a basic arithmetic exercise over 40 ft². What current does that represent?

Known values:

• J = 10 mA/ft²
• A = 40 ft²
• I = ?

Use:

Substitute:

Calculate:

Convert if needed:

Answer: The current is 400 mA, or 0.400 A.

Field meaning: This shows the arithmetic relationship between current density, area, and current. It does not prescribe that 10 mA/ft² is a required design value.

Worked Example 4 — Total Area versus Exposed Area

A structure has a total area of 1,000 ft², but an estimate uses 5% exposed area. A current of 2 amps is applied to the estimated exposed area. What current density is calculated using the exposed area?

Known values:

• total area = 1,000 ft²
• exposed area estimate = 5%
• current = 2 A

Calculate exposed area:

Use:

Substitute:

Calculate:

Answer: The current density using the estimated exposed area is 0.04 A/ft².

Field meaning: Changing the assumed area changes the current density. The exposed-area percentage is an assumption, not a universal rule.

Common Mistakes

1. Confusing current density with total current. Current density is current per unit area. Total current is just current.
2. Using total area when exposed area was intended. The selected area strongly affects the result.
3. Treating an assumed area as a fact. Exposed or bare area may be estimated.
4. Mixing amps and milliamps without tracking units. A/ft² and mA/ft² are different units.
5. Mixing square feet and square meters. Keep area units consistent.
6. Prescribing design values without source support. This page teaches the calculation only.
7. Assuming current density proves protection. CP protection must be evaluated with proper field measurements and criteria.
8. Using too many decimals. Current-density estimates often depend on approximate area assumptions.

Practice Problems

1. A current of 4 A is applied to 200 ft². What is the current density in A/ft²?
2. A current of 300 mA is applied to 30 ft². What is the current density in mA/ft²?
3. A current density of 5 mA/ft² is used in a basic arithmetic exercise over 100 ft². What current does that represent?
4. Convert 750 mA to amps.
5. A total area is 2,000 ft². If 2% is assumed exposed, what exposed area is used?
6. A current of 3 A is applied to an estimated exposed area of 60 ft². What is the current density in A/ft²?
7. If the same current is spread over a larger area, does current density increase or decrease?
8. Does current density by itself prove that a structure satisfies CP protection criteria?

Practice Problem Answer Key

Related Learning

• Pipeline Surface Area
• Tank Bottom Surface Area
• Current Requirement
• Soil Resistivity

Related Formulas

• Pipeline Surface Area
• Tank Bottom Surface Area
• Current Requirement
• Ohm's Law