Match the diagram conditions, then follow the example inputs and results. Change numerical values in the calculator.
1. Match the diagram to your question
圧縮コイルばねを横から見た説明です。線径と平均コイル径を見分けます。
dは線径、Dはコイル中心線間の平均径です。巻数と材料Gも確認します。
線径 d
2 mm
平均コイル径 D（外径−線径）
20 mm
有効巻数 Na
6
総巻数 Nt
8
横弾性係数 G（入力例）
77 GPa
圧縮荷重 F
50 N
自由長 L
50 mm
橙のδが荷重による縮みです。密着に達した後へ、この線形の結果を延長しないでください。
ばね定数 k
3.20833 N/mm
δ · 線形モデルの圧縮量 δ
15.5844 mm
補正したせん断応力
364.412 MPa
A compression spring is shown from the side. Distinguish wire diameter from mean coil diameter.
d is wire diameter; D is mean diameter between wire centre lines. Also check coil counts and material G.
Wire diameter d
2 mm
Mean coil diameter D (outside minus wire)
20 mm
Active coils Na
6
Total coils Nt
8
Shear modulus G (example)
77 GPa
Compression force F
50 N
Free length L
50 mm
Orange δ is compression under load. Do not extend this linear result beyond coil bind.
Spring rate k
3.20833 N/mm
δ · Linear-model compression δ
15.5844 mm
Corrected shear stress
364.412 MPa
Blue marks inputs; orange marks outputs. These diagrams explain the fixed example below; dimensions and deformation are not drawn to physical scale.
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2. Example inputs
Wire diameter dWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
2 mm
Mean coil diameter D (outside minus wire)What goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
20 mm
Active coils NaWhat goes here?
Match the field symbol to the diagram and check dimensions, specifications or operating conditions. Replace example numbers with your actual conditions.
6
Total coils NtWhat goes here?
Match the field symbol to the diagram and check dimensions, specifications or operating conditions. Replace example numbers with your actual conditions.
8
Shear modulus G (example)What goes here?
E describes axial stiffness and G shear stiffness; neither is yield strength or allowable stress.
Use the actual material, temperature and direction. Table entries are comparisons, not material specifications. For isotropic elasticity, check consistency with G=E/[2(1+ν)].
Choose values for actual contact, lubrication, temperature and other conditions. These initial values are examples.
77 GPa
Compression force FWhat goes here?
Magnitude of a push or pull, in force units such as N, rather than mass in kg.
50 N
Free length LWhat goes here?
Use the dimension marked in the diagram. Distinguish radius from diameter, bore from outside diameter, and overall length from support span.
50 mm
These are fixed teaching inputs. Coefficients, properties and comparison limits are not recommendations. Enter your conditions in the calculator.
3. Results for this example
Spring rate k
3.20833 N/mm
Linear-model compression δ
15.5844 mm
Corrected shear stress
364.412 MPa
Spring rate relates force to compression. Beyond coil bind, the linear deflection no longer describes behavior. Distinguish mean coil diameter from outside diameter.
4. Which formula is used?
k = Gd⁴/(8D³Na); δ=F/k; C=D/d; Kw=(4C−1)/(4C−4)+0.615/C; τ=Kw 8FD/(πd³)
Table units are not always the units required in the formula. The calculator converts selected units to its internal base units before computing.
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Assumptions and exclusions
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.
