Coastal Erosion Calculator
Design cathodic protection systems for submerged steel structures using sacrificial anodes. Calculate current demand, anode mass, count, and resistance per DNV-RP-B401.
About this calculator
Submerged steel corrodes electrochemically, and galvanic cathodic protection counters that by attaching sacrificial anodes (typically aluminum-zinc-indium alloy) that corrode preferentially, feeding protective current into the structure. This calculator's current-demand, anode-mass, and anode-resistance methodology follows DNV-RP-B401, DNV's recommended practice for cathodic protection design using aluminum or zinc based galvanic anodes. It starts from a required current density — how much protective current each square meter of bare steel needs — multiplies by the total exposed surface area to get total current demand, then integrates that demand over the full design life in hours (years × 8760) to get total charge in amp-hours.
Dividing that charge by the anode material's electrochemical capacity (amp-hours per kilogram, adjusted by a utilization factor since an anode can't be consumed down to nothing before it stops working reliably) gives the total anode mass needed, which is then divided by the mass of a single anode and rounded up to a whole anode count. Separately, it checks that the anodes can actually deliver enough current: each anode's resistance in seawater is estimated with the Dwight formula for a slender rod, the anodes are combined as parallel resistances, and a typical driving voltage of about 0.25 V (the potential difference between an aluminum anode and protected steel) is divided by that resistance to get available current — reported as a capacity ratio against the required current, which must stay above 1.0 for the design to actually work electrically, not just have enough total mass. A key assumption is a constant current density over the whole design life; real designs often apply higher initial/final density factors and a coating breakdown factor that increases demand as any coating degrades over time, neither of which this simplified model varies explicitly.
Inputs
Results
Total current demand (A)
60
Total anode mass required (kg)
8,212.5
Number of anodes
33
Figures current as of 2021. Source: DNV, Recommended Practice DNV-RP-B401, Cathodic Protection Design, edition 2021-05
How to Use This Calculator
- Enter bare steel area (m2) requiring cathodic protection.
- Enter design current density (mA/m2) for the environment: tropical ~150, temperate ~100, arctic ~80.
- Enter design life (years), anode capacity (Ah/kg), and mass per anode (kg).
- Read total current required (A), number of anodes needed, and total anode mass (kg).
- Verify anode spacing and coverage meets DNV-RP-B401 or project specification requirements.
How the result changes with Bare steel area (m²)
| Bare steel area (m²) | Total current demand (A) | Total anode mass required (kg) | Number of anodes |
|---|---|---|---|
| 250 | 30 | 4,106.3 | 17 |
| 375 | 45 | 6,159.4 | 25 |
| 750 | 90 | 12,318.8 | 50 |
| 1,250 | 150 | 20,531.3 | 83 |
What each input means
- Bare steel area (m²)
- Total exposed (uncoated) steel surface area requiring protection.
- Current density (mA/m²)
- Design mean current density. Tropical ~150, temperate ~100, arctic ~80 mA/m².
- Design life (years)
- Required cathodic protection design life.
- Anode capacity (Ah/kg)
- Electrochemical capacity. Al-Zn-In ~2000, Zn ~780 Ah/kg.
- Mass per anode (kg)
- Net mass of a single sacrificial anode.
- Utilization factor
- Anode utilization factor u (typically 0.8-0.9).
- Anode length (m)
- Length of anode for resistance calculation (Dwight formula).
- Anode effective radius (m)
- Effective radius of anode cross-section.
- Seawater resistivity (Ω·m)
- Electrical resistivity of seawater. Typical 0.2-0.35 Ω·m.
What each result means
- Total current demand (A)
- Required protection current for the entire structure.
- Total anode mass required (kg)
- Minimum anode material mass to last the design life.
- Number of anodes
- Minimum number of anodes (rounded up).
- Actual mass installed (kg)
- Total mass of whole anodes as installed.
- Single anode resistance (Ω)
- Electrical resistance of one anode in seawater (Dwight formula).
- Total circuit resistance (Ω)
- Parallel resistance of all anodes.
- Current capacity ratio
- Ratio of available current to required current. Must exceed 1.0 for adequate protection.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersBare steel area (m²) = 500, Current density (mA/m²) = 120, Design life (years) = 25, Anode capacity (Ah/kg) = 2000 = 9 input(s) provided
- Calculate Total current demandTotal current demand = (surfaceArea * currentDensity) / 100060 = 60
- Calculate Total anode mass requiredTotal anode mass required = totalCharge / (utilFactor * anodeCapacity)8212.5 = 8212.5
- Calculate Number of anodesNumber of anodes = ceil(totalAnodeMass / anodeMassEach)33 = 33
- Calculate Actual mass installedActual mass installed = numAnodes * anodeMassEach8250 = 8250
- Calculate Single anode resistanceSingle anode resistance = (rhoSW / (2 * π * L)) * (ln((4 * L) / r) - 1)0.1361 = 0.1361
Figures and sources
- Galvanic (sacrificial) anode cathodic protection design methodology — current demand, anode mass, and anode resistance (2021) — DNV, Recommended Practice DNV-RP-B401, Cathodic Protection Design, edition 2021-05
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does the calculator apply a utilization factor to the anode's electrochemical capacity?
An anode's rated capacity in amp-hours per kilogram assumes it could be consumed completely, but in practice an anode stops making reliable electrical contact with its support structure and delivering current effectively once a significant fraction of its material is gone. The utilization factor (typically 0.8–0.9) discounts the rated capacity to reflect only the usable fraction of the anode's mass, so the calculated total anode mass required already builds in a margin for material that won't actually be consumed before the anode needs replacing.
What does the current capacity ratio tell me that the anode mass total doesn't?
Total anode mass only confirms there's enough material to last the design life electrochemically — it says nothing about whether the anodes can physically push that much current into the seawater fast enough. The capacity ratio divides available current (driving voltage over the anodes' combined parallel resistance) by required current demand; a ratio below 1.0 means the anodes would run out of current-delivering capability even though they have plenty of remaining material, which usually means adding more anodes rather than just more mass per anode.
Why does anode resistance decrease when I add more anodes?
Multiple anodes protecting the same structure act as parallel electrical resistors, and resistances in parallel always combine to something lower than any single resistance. This calculator divides the single anode's Dwight-formula resistance by the anode count to get total circuit resistance, which is why increasing the number of anodes (even without increasing total mass) directly improves the current capacity ratio — more anodes means more parallel current paths, not just more total sacrificial material.
Why does the design assume constant current density instead of it varying over the design life?
Real cathodic protection systems typically need a higher initial current density to establish protective calcium-carbonate scale on bare steel, a lower mean density once that scale forms, and a higher final density as anodes near depletion and any coating degrades — DNV's Recommended Practice DNV-RP-B401 (Cathodic Protection Design) accounts for all three phases separately. This calculator simplifies to one representative mean current density applied uniformly across the full design life, which is a reasonable planning estimate but should be checked against a phase-specific design current density table for a bankable engineering design.
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