Parallel Axis Theorem Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mechanical, Civil & Structural Engineering — Statics/Dynamics, Strength of Materials, Machine Design, Civil, HVAC, Vibration

Tranche

tranche-4

Evidence ID

t4-010

Ledger rows

1

No ledger note is attached.

Review findings

Formula is mathematically standard but the instrument specification is ambiguous about area moment of inertia versus mass moment of inertia, the required parallel-axis condition, and whether inputs describe one component or a complete composite section. The honest label should explicitly say 'Area Moment of Inertia (Second Moment of Area) about a Parallel Shifted Axis' and should document the composite summation rule.

Formula and scope findings

• I=I_c+Ad² is correct for the second moment of area of one component about an axis parallel to its centroidal axis, with d measured perpendicular to the axes.
• For a composite section, the formula must be applied and summed component-by-component: I=Σ(I_ci+A_i d_i²). Holes require signed component areas and centroidal inertias.
• The term 'moment of inertia' is ambiguous: this formula computes area moment of inertia (second moment of area), not mass moment of inertia.
• The spec does not state that I_c is the centroidal second moment of area or that the shifted axis is parallel to the centroidal axis.

Unit assumptions

• I_c and the output I use units of length⁴.
• A uses units of length² and d uses units of length; all three inputs must use mutually consistent length units.
• d is the perpendicular distance between parallel axes and is treated as a nonnegative distance; squaring makes the sign irrelevant mathematically.
• If SI units are used, A in m², d in m, and I_c/I in m⁴ are required.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

An extreme but representable-looking input causes the plain JavaScript arithmetic to overflow A d² to Infinity. The calculator should reject or flag non-finite inputs and outputs. The specification has no denominator trap and no genuine formula regime switch.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "I_c": 200000,
    "A": 6000,
    "d": 50,
    "units": "mm⁴, mm², mm"
  },
  "expected_outputs": {
    "I": 15200000,
    "units": "mm⁴"
  },
  "working": "d² = 50² = 2,500 mm². Ad² = 6,000 × 2,500 = 15,000,000 mm⁴. I = I_c + Ad² = 200,000 + 15,000,000 = 15,200,000 mm⁴."
}

Related workflows

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json