ENGINEERING CALCULATORS
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Engineering calculators (Beta)
Find area, centroid, second moments and elastic section moduli from dimensions.
Click the grid to add ordered vertices. Edit coordinates in mm; separate holes with a blank line. The last vertex closes to the first automatically.
Choose units and enter numbers. Full-width digits and fractions such as 1/8 or 1 3/8 are accepted. Changing a unit converts the entered value.
Reference calculation only. Results do not certify suitability for an actual design or its safety.
Inputs: select a blue symbol to edit Results: red-orange values and lines
3D shows an illustrative extrusion. Its display length does not enter the section calculations. Edit dimensions in 2D.
A = ΣAi, x̄ = ΣAi xi / A, Ix = Σ(Ixi + Ai Δyi²), Z = I / c, r = √(I / A)
Displayed values are rounded. Diagrams illustrate the calculation conditions. Initial material and fluid properties are examples; replace them with values for the actual material, temperature and conditions.
ReferenceEquations assume particular loads, supports and deformation ranges. Check inputs, units and the applicability of each equation. Diagrams explain conditions; they are not manufacturing drawings or proof of safety.
Material values are typical values or reference ranges, not certified product properties or ready-to-use design allowables. They vary with standards, product form, dimensions, temper and temperature. Check the specifications and inspection certificates for the actual product.
Displayed safety factors and checks apply only to the supplied inputs and calculation model. They do not automatically establish the safety of a complete design, including code compliance, service life, fatigue or joints. For actual design, manufacture and use, separately verify applicable regulations and standards, product specifications, and the necessary tests and engineering review.
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断面形状と寸法から、面積・重心・I・Zを求めます。
選択した形状・計算方法により、使う項目は変わります。実際の計算は上の図と入力欄で行えます。
A = ΣAi, x̄ = ΣAi xi / A, Ix = Σ(Ixi + Ai Δyi²), Z = I / c, r = √(I / A)
理想寸法の均質断面です。圧延材の丸み・フィレット・テーパー・局部座屈・塑性断面係数は含みません。Zは弾性断面係数です。L形のようにIxy≠0の断面は、主軸特性は表示しますが、基本の梁・座屈計算へは直接連携しません。自由断面は直線で囲まれた外周と穴に対応します。
現在選択中の方法には、操作欄の「計算式・適用条件」を使ってください。参考計算であり、設計全体の安全性を保証するものではありません。
Find area, centroid, second moments and elastic section moduli from dimensions.
The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.
A = ΣAi, x̄ = ΣAi xi / A, Ix = Σ(Ixi + Ai Δyi²), Z = I / c, r = √(I / A)
Ideal homogeneous sections without corner radii, fillets, taper, local buckling or plastic section properties. Z is the elastic section modulus. Principal properties are displayed, but unsymmetric sections with nonzero Ixy do not feed the basic beam or column calculation directly. Free sections use straight polygon edges and holes.
The displayed formula and conditions in the working panel apply to the currently selected model. Reference calculation only; it does not certify a complete design.
図で条件を整理してから計算し、最後に実際の部品仕様を確認します。
Understand conditions with diagrams, calculate, then verify actual specifications.
同じ材料・支持・荷重条件の梁では、断面二次モーメントIはたわみに、弾性断面係数Zは曲げによる縁応力に使います。Iの単位はmm⁴、Zはmm³です。選んだ曲げ軸と結果の添字を合わせてください。
断面の重心を通る主軸についての単純な曲げではσ = M/Zです。MをN·mm、Zをmm³でそろえるとσはN/mm²（MPa）になります。非対称断面や斜め曲げを、軸を合わせずにこの式へ入れることはできません。
幅B = 40 mm、高さH = 20 mmの均質な長方形を、重心x軸まわりに曲げる例です。Ix = BH³/12 = 26,666.666… mm⁴、Zx = BH²/6 = 2,666.666… mm³になります。
90°回してB = 20 mm、H = 40 mmにすると、同じ曲げ軸に対してI = 106,666.666… mm⁴、Z = 5,333.333… mm³です。面積はどちらも800 mm²ですが、Iは4倍、Zは2倍。材料・長さ・荷重・支持を同じにした理想梁なら、たわみは1/4、同じ曲げモーメントによる縁応力は1/2になります。
1 cm⁴ = 10,000 mm⁴、1 cm³ = 1,000 mm³です。IとZでは換算倍率も違います。圧延材の丸みなどを含むカタログ値と、この画面の理想寸法からの計算値は、形状の前提をそろえて比較します。
For otherwise identical beam material, supports and loading, second moment of area I is used in deflection calculations; elastic section modulus Z is used for bending stress at an edge. I is in mm⁴ and Z in mm³. Match the bending axis to the result subscript.
For simple bending about a centroidal principal axis, σ = M/Z. Using N·mm for M and mm³ for Z gives N/mm² (MPa). Do not apply this simple relation to an arbitrary unsymmetric section or oblique bending without resolving the axes.
Take a homogeneous rectangle with width B = 40 mm and height H = 20 mm, bending about its centroidal x axis. Ix = BH³/12 = 26,666.666… mm⁴ and Zx = BH²/6 = 2,666.666… mm³.
Turning it to B = 20 mm and H = 40 mm gives I = 106,666.666… mm⁴ and Z = 5,333.333… mm³ about the same bending direction. Both areas are 800 mm², but I increases fourfold and Z doubles. With identical material, length, load and supports in the ideal beam model, deflection becomes one quarter and edge stress under the same moment becomes one half.
1 cm⁴ = 10,000 mm⁴, while 1 cm³ = 1,000 mm³. I and Z use different conversion factors. Catalogue values can include rolled corner radii; compare them with this ideal-dimension calculation only after matching the section assumptions.
Convert I units → · Convert Z units → · Calculate beam deflection with supports and loads →
