Grain Stability Calculation: Formulas and Worked Example

The three grain stability criteria

For the standard International Grain Code A 7.1 assessment:

The residual-area calculation ends at the earliest of 40°, the flooding angle, or the angle where the difference between GZ and the heeling arm is greatest. The starting point is the first equilibrium intersection of the two curves.

These checks apply throughout the voyage. Check the relevant departure, arrival and intermediate conditions; the lowest displacement is not automatically the worst condition.

Reference: International Grain Code, A 7.1 and figure A7. This page follows the standard A 7 method; other authorised arrangements must follow their own approved conditions.

Grain stability formulas and units

1. Convert volumetric moment into a weight moment

• VHM: volumetric heeling moment, in m⁴.
• SF: stowage factor, in m³/t.
• C: the correction factor required by the table and centre-of-gravity assumptions.
• H: total grain heeling moment, in t·m.

The units explain why you divide: m⁴ ÷ (m³/t) = t·m. If holds have different stowage factors, calculate each hold separately before adding the moments.

2. Correct GM for liquid free surfaces

Δ is the ship’s total displacement in tonnes. Liquid free-surface moments and grain heeling moments are separate parts of the calculation.

3. Construct the grain heeling-arm line

Plot these two lever values, in metres, at 0° and 40° and join them with a straight line. Between these angles, linear interpolation gives λθ = λ₀ × (1 − θ/200), with θ in degrees.

Calculation reference: AMSA grain stability form, tables 3, 6 and 10.

When do you use 1.06 or 1.12?

These factors allow for the adverse vertical movement of the grain surface under the specified calculation method.

• 1.06: relevant to the authorised filled, trimmed calculation using cargo centres adjusted for underdeck voids.
• 1.12: used for the usual partly filled calculation when this grain vertical-shift allowance remains to be applied.
• 1.00: used in the example below for filled holds assessed using the specified full-compartment volumetric centres.

Read the table notes and centre-of-gravity basis. A factor may already be included in the supplied moments, or an approved alternative may account for the effect. Do not add a second correction.

References: AMSA table 3 correction notes and MSC.552(108), amended B 1.5.

2026 update: MSC.552(108) adds a specially suitable, partly filled compartment condition for grain loaded in way of the hatch opening with ends untrimmed. Use the approved classification and matching tables; do not treat it as an ordinary filled hold. Read the amendment, effective 1 January 2026.

Find the angle of heel from the curves

Plot the corrected GZ curve for the same loading condition and the grain heeling-arm line on the same axes. The first intersection gives the equilibrium heel after the assumed grain shift.

In this example, the supplied training GZ curve first meets the heeling-arm line at 10°, where both levers are 0.190 m.

The assumed deck-edge immersion angle is 16°. Because this example ship was constructed in 2005, its permitted heel is the smaller of 12° and 16°: 12°.

The GZ values used here already include the specified liquid free-surface allowance. For a question starting with KN tables, see how to calculate GZ from KN and follow the stated correction method.

Calculate the residual area using Simpson’s rule

Step 1 — Choose the correct interval

For this example, assume flooding begins at 55°. The complete example curves have their greatest separation at about 41.5°. The earliest limit is therefore 40°.

Calculate the positive area from the equilibrium heel at 10° to 40°. At each selected angle, subtract the heeling arm from GZ:

Step 2 — Tabulate equally spaced ordinates

Use a 5° interval, giving six intervals and seven ordinates. The corrected GZ values below are supplied training data, rounded to four decimal places.

Step 3 — Apply Simpson’s rule in radians

Sum of products = 4.3518.
Interval h = 5 × π/180 = 0.087266 rad.

The area margin is approximately 0.0516 m·rad. Simpson’s rule is a numerical estimate; use adequate ordinates for the actual curve. Its starting ordinate must be at the intersection, even when that angle is not a multiple of 5°.

Result for this example condition

This illustrative condition satisfies the three checks. A voyage assessment must also cover the other required loading conditions and the vessel’s remaining loading limits.

Using a maximum allowable heeling moment table

An approved table can provide the limiting grain heeling moment for the relevant displacement and KG or GM. Read its input definitions, correction basis and trim limits before interpolating.

Suppose a training table at 20,000 t, expressly using fluid KG, gives:

At KG fluid = 6.90 m, the interpolation fraction is (6.90 − 6.80) ÷ (7.00 − 6.80) = 0.5.

Actual H = 4,000 t·m, so the moment is within this example limit by 400 t·m.

This is a separate illustrative table. Use the approved table method where it demonstrates the applicable criteria; do not substitute an assumed limit or use solid KG in a table that requires fluid KG.

Reference: AMSA table 7, maximum allowable heeling moments.

Common mistakes in grain stability calculations

• Multiplying VHM by stowage factor. With SF in m³/t, divide VHM by SF.
• Mixing m⁴ and t·m. Convert all hold moments to the same units before adding or comparing them.
• Using one SF for different cargoes. Work hold by hold.
• Applying 1.06 or 1.12 automatically. Check the cargo-centre assumptions and corrections already included.
• Stopping after the GM check. A satisfactory GM alone does not establish grain compliance.
• Calculating the whole area under GZ. Use the positive residual area above the heeling-arm line, from the first intersection to the applicable limit.
• Always using 40° as the endpoint. Flooding or maximum separation may occur earlier.
• Using degrees without converting the area. Multiply an area in metre-degrees by π/180 to obtain metre-radians.

Short answers for revision

What is the difference between a heeling moment and a heeling arm?

A moment is measured in t·m. Dividing it by displacement gives an arm in metres. Compare arms on a GZ graph and moments against an allowable-moment table.

Is the flooding angle the same as deck-edge immersion?

No. They describe different events and serve different checks: deck-edge immersion may restrict the permitted heel, while the flooding angle can restrict the residual-area interval.

Is grain stability the same calculation as free-surface correction?

No. The grain heeling assessment and the liquid free-surface allowance are both needed in the relevant calculation. Revise the liquid correction in our Free Surface Effect guide.