Tank Bottom Surface Area for Cathodic Protection
Tank bottom surface area is the area of the circular bottom of a tank.
In cathodic protection work, tank bottom area may be used as a starting point for basic estimates involving protected area, current density, and current requirement discussions. The calculation is geometry. It does not prove tank protection and it does not replace field measurements, design review, or criteria evaluation.
Quick Definition
For a circular tank bottom, area may be calculated from radius:
A = π × r2
or from diameter:
A = (π × D2) ÷ 4
Where:
- A is tank bottom area.
- π is pi, approximately 3.1416.
- r is radius.
- D is diameter.
Radius and diameter must use the same length units you want squared in the answer.
When Tank Bottom Area Is Used in CP Work
Tank bottom area may be used when estimating:
- tank bottom area;
- protected area;
- current density when current and area are known;
- basic current requirement discussions;
- comparison of tank sizes.
This page explains the area calculation only. It does not teach AST or UST protection criteria and does not say what current density value should be used for design.
Formula Reference
| Known value | Formula | Use when |
|---|---|---|
| Radius | A = π × r2 | radius is known |
| Diameter | A = (π × D2) ÷ 4 | diameter is known |
| Diameter from radius | D = 2 × r | radius is known |
| Radius from diameter | r = D ÷ 2 | diameter is known |
Variable and Unit Table
| Symbol | Meaning | Common unit | Unit symbol | CP field meaning |
|---|---|---|---|---|
| A | Tank bottom area | square feet or square meters | ft2 or m2 | Circular bottom area used in area and current-density estimates |
| π | Pi | unitless | — | Approximately 3.1416 |
| r | Radius | feet or meters | ft or m | Distance from tank center to tank edge |
| D | Diameter | feet or meters | ft or m | Full width across the circular tank bottom |
Use matching units before calculating: if radius or diameter is in feet, area will be in square feet; if radius or diameter is in meters, area will be in square meters; if diameter is given in inches, convert it to feet before calculating square feet.
Common Conversion
- 1 ft = 12 in
- diameter in feet = diameter in inches ÷ 12
How to Use the Formula
Use A = π × r2 when radius is known.
Use A = (π × D2) ÷ 4 when diameter is known.
Do not use diameter as radius. Radius is half of diameter.
For square feet:
- use radius or diameter in feet;
- square the radius or diameter as required by the formula;
- report the answer in ft2.
This calculation gives the circular bottom area. It does not define coating condition, exposed area, current requirement, or protection status.
Worked Example 1 — Area from Radius
A circular tank bottom has a radius of 10 ft. What is the tank bottom area?
Known values:
- r = 10 ft
- π = 3.1416
- A = ?
Use:
A = π × r2
Substitute:
A = 3.1416 × (10 ft)2
Calculate:
A = 3.1416 × 100 ft2
A = 314.16 ft2
Answer: The tank bottom area is approximately 314 ft2.
Field meaning: This is the circular bottom area. It does not determine whether the tank is protected.
Worked Example 2 — Area from Diameter
A circular tank bottom has a diameter of 40 ft. What is the tank bottom area?
Known values:
- D = 40 ft
- π = 3.1416
- A = ?
Use:
A = (π × D2) ÷ 4
Substitute:
A = (3.1416 × (40 ft)2) ÷ 4
Calculate:
A = (3.1416 × 1600 ft2) ÷ 4
A = 1,256.64 ft2
Answer: The tank bottom area is approximately 1,257 ft2.
Field meaning: The diameter formula is useful when tank diameter is known from drawings or field records.
Worked Example 3 — Convert Diameter from Inches
A small circular tank bottom has a diameter of 120 inches. What is the tank bottom area in square feet?
Known values:
- D = 120 in
- A = ?
Convert diameter first:
120 in ÷ 12 = 10 ft
Use:
A = (π × D2) ÷ 4
Substitute:
A = (3.1416 × (10 ft)2) ÷ 4
Calculate:
A = (3.1416 × 100 ft2) ÷ 4
A = 78.54 ft2
Answer: The tank bottom area is approximately 78.5 ft2.
Field meaning: Convert inches to feet before calculating square feet.
Worked Example 4 — Compare Two Tank Diameters
Tank A has a diameter of 20 ft. Tank B has a diameter of 40 ft. What are their approximate bottom areas?
Tank A:
A = (3.1416 × (20 ft)2) ÷ 4
A = 314.16 ft2
Tank B:
A = (3.1416 × (40 ft)2) ÷ 4
A = 1,256.64 ft2
Answer: Tank A is approximately 314 ft2. Tank B is approximately 1,257 ft2.
Field meaning: Doubling diameter does not just double area. Because diameter is squared in the formula, the larger tank has much more bottom area.
Common Mistakes
- Using diameter as radius. Radius is half the diameter.
- Forgetting to square the radius or diameter. Area formulas require a squared length.
- Using inches with feet without converting. Convert inches to feet before calculating square feet.
- Forgetting square units. The answer is area, such as ft2 or m2.
- Assuming tank bottom area equals exposed area. Area and exposed/bare area are not automatically the same.
- Treating area calculation as CP criteria evaluation. Area supports estimates. It does not prove protection.
- Applying AST or UST criteria from this page. This page does not teach tank CP criteria.
- Using too many decimals. Area estimates are usually approximate.
Practice Problems
- A circular tank bottom has a radius of 5 ft. What is the area?
- A circular tank bottom has a radius of 12 ft. What is the area?
- A circular tank bottom has a diameter of 20 ft. What is the area?
- A circular tank bottom has a diameter of 50 ft. What is the area?
- A circular tank bottom has a diameter of 96 inches. What is the diameter in feet?
- A circular tank bottom has a diameter of 96 inches. What is the bottom area in square feet?
- If a tank diameter doubles, does the bottom area simply double?
- Does tank bottom area by itself prove that a tank satisfies CP protection criteria?
Practice Problem Answer Key
| Problem | Answer | Calculation / explanation |
|---|---|---|
| 1 | 78.5 ft2 | A = 3.1416 × 52 = 78.54 ft2 |
| 2 | 452 ft2 | A = 3.1416 × 122 = 452.39 ft2 |
| 3 | 314 ft2 | A = (3.1416 × 202) ÷ 4 = 314.16 ft2 |
| 4 | 1,963 ft2 | A = (3.1416 × 502) ÷ 4 = 1,963.5 ft2 |
| 5 | 8 ft | 96 in ÷ 12 = 8 ft |
| 6 | 50.3 ft2 | A = (3.1416 × 82) ÷ 4 = 50.27 ft2 |
| 7 | No | Area changes with the square of diameter. Doubling diameter makes the area four times larger. |
| 8 | No | Area supports estimates. CP protection must be evaluated with proper measurements and criteria. |