Metal Profile Theoretical Mass Worksheet
Calculate mass from ideal sharp-corner cross-sectional geometry,length and a documented material density. Use millimetres with kg/m³ or inches with lb/in³;the worksheet converts internally to SI and reports both kg and avoirdupois pounds.
Document one ideal prismatic part
Select units and profile first. Changing either selector reinterprets—not converts—numbers already entered. Use drawing dimensions and density for the actual alloy,condition and temperature.
Part mass
Mass per length
Ideal cross-section area
Ideal volume
Density used
Profile model
Cross-section equations
| プロフィール | Ideal area A | Geometry boundary |
|---|---|---|
| solid round | πd²/4 | d is diameter. |
| hollow round | π[OD²−(OD−2t)²]/4 | 0<t<OD/2. |
| rectangle/flat | w t | Sharp rectangle. |
| solid square | s² | s is side. |
| regular hex by across-flats F | √3 F²/2 | F is distance between opposite flats. If side length a is used,the different formula is3√3a²/2. |
| unequal angle | A tA+(B−tA)tB | Two sharp rectangles with one overlap removed;tA<B and tB<A. |
| チャンネル | h tw+2(b−tw)tf | Sharp web plus two flange extensions;tw<b and2tf<h. |
Internal dimensions use millimetres. V=A L in mm³ and m=ρV/10⁹ in kg when ρ is kg/m³. Exact conversions use1in=25.4mm,1ft=0.3048m and1avoirdupois lb=0.45359237kg.
Sources and applicability
BIPM SI Brochure,9th edition (2019),updated2026 establishes the SI framework and kilogram as the mass unit. NIST SP811 AppendixB documents exact international-inch and avoirdupois-pound conversions used in the unit-invariance tests.
NIST mass guidance distinguishes mass from weight-force. Density values are not universal constants for broad labels such as “steel” or “aluminium”;this worksheet therefore requires the user to enter and cite the value applicable to the exact material and condition.
The geometry equations are general Euclidean/engineering relations,not ISO formulas. The former related-link label “ISO1940” was outdated:ISO’s lifecycle records mark ISO1940-1:2003 withdrawn and revised by ISO21940-11:2016 with Amendment1:2022. This page does not calculate residual unbalance or a balance tolerance.
修正内容
The former hex-bar input was explicitly flat-to-flat,but the code used 3√3F²/2,the formula for hexagon side length. For a true across-flats value the correct area is √3F²/2;the former result was exactly three times too large. The replacement also enforces hollow-tube,angle and channel geometry constraints.
kg and lb outputs are now labelled mass,with lb explicitly avoirdupois. The rounded coefficient2.20462 was replaced by division by the exact international-pound definition. Generic density presets,pre-filled dimensions,quick presets and local history were removed;the density and its source are now required. Outputs describe theoretical nominal geometry and no longer imply actual procurement or lifting weight.
