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Compression spring rate & stress calculator

Engineering calculators (Beta)

Find round-wire compression spring rate, deflection and Wahl-corrected stress.

Inputs

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.

Results

Reference calculation only. Results do not certify suitability for an actual design or its safety.

Diagram

Inputs: select a blue symbol to edit Results: red-orange values and lines

Formula and applicability

k = Gd⁴/(8D³Na); δ=F/k; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw 8FD/(πd³)

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.

Reference
Using this information as a reference

Equations 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.

この計算で求められること

丸線コイルの寸法から、ばね定数・たわみ・Wahl補正応力を求めます。

入力・結果・適用条件を確認する

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。

主な入力

  • 線径 d (mm / cm / m)
  • 平均コイル径 D(外径−線径) (mm / cm / m)
  • 有効巻数 Na (—)
  • 総巻数 Nt (—)
  • 横弾性係数 G(入力例) (GPa / MPa / Pa)
  • 圧縮荷重 F (N / kN / mN)
  • 自由長 L (mm / cm / m)

得られる結果

  • ばね定数 k (N/mm)
  • 線形モデルの圧縮量 δ (mm)
  • ばね指数 C (—)
  • Wahl補正係数 (—)
  • 補正したせん断応力 (MPa)
  • 密着高さの簡易値 Nt d (mm)
  • 密着までの残り量(負は適用外) (mm)

計算式の概要

k = Gd⁴/(8D³Na); δ=F/k; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw 8FD/(πd³)

円形丸線・小さいピッチ角・線形弾性の圧縮コイルばねです。密着高さは総巻数×線径の簡易値で、座面の仕上げによる補正は含みません。疲労・許容応力・座屈・共振・製造公差・密着後の挙動は計算しません。

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。

関連する計算

What this calculator does

Find round-wire compression spring rate, deflection and Wahl-corrected stress.

Inputs, outputs and applicability

The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.

Inputs

  • Wire diameter d (mm / cm / m)
  • Mean coil diameter D (outside minus wire) (mm / cm / m)
  • Active coils Na (—)
  • Total coils Nt (—)
  • Shear modulus G (example) (GPa / MPa / Pa)
  • Compression force F (N / kN / mN)
  • Free length L (mm / cm / m)

Calculated results

  • Spring rate k (N/mm)
  • Linear-model compression δ (mm)
  • Spring index C (—)
  • Wahl correction factor (—)
  • Corrected shear stress (MPa)
  • Approximate solid height Nt d (mm)
  • Remaining travel to solid (negative: outside model) (mm)

Formula overview

k = Gd⁴/(8D³Na); δ=F/k; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw 8FD/(πd³)

Round-wire, small-helix-angle linear-elastic compression spring. Solid height is approximated as total coils times wire diameter without end-finish corrections. Fatigue, allowable stress, buckling, resonance, manufacturing tolerances and behavior after coil bind are excluded.

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.

Related tools

Extension coil spring load and rate calculator →
Torsion coil spring torque and body stress calculator →
Cantilever leaf spring load and deflection calculator →

数値の感覚を、図と動きで確かめる

説明用の別モデルです。適用条件を確認してください。数値は自動転記しません。

See the idea in diagrams and motion

A separate explanatory model. Check its assumptions; values are not transferred.