Two figures in, a clear answer out. The spring calculator uses elasticity module (m), number of active coils (na), achieved torsion angle (α), number of body coils (nb), extension/compression δx, distance of lever arm (r), length, first end (l1), length, second end (l2), outer diameter (od), pitch, modulus of rigidity (g) and spring index c to produce force applied to the spring (f), free length for squared and ground end and torque applied to the spring (m), applying the standard relationship for this problem in the order the calculation actually needs it.
What Is the Spring Calculator?
This spring calculator is for the kind of problem where you know the physical quantities but not the number you need. It turns elasticity module (m), number of active coils (na), achieved torsion angle (α), number of body coils (nb), extension/compression δx, distance of lever arm (r), length, first end (l1), length, second end (l2), outer diameter (od), pitch, modulus of rigidity (g) and spring index c into force applied to the spring (f), free length for squared and ground end and torque applied to the spring (m).
Physics calculations go wrong in predictable ways, usually through mixing units or dropping a digit. Work through the result one step at a time and check that the figures are the size you would expect at each stage.
How the Spring Physics Works
The relationship is applied step by step, and each step is a standard piece of physics rather than a single opaque formula. That means you can check the intermediate values against what the theory predicts, which is usually faster than checking only the final answer.
Keep every value in the same unit system throughout the calculation. Mixing metres and feet part way through is the single most common reason a correct formula gives a wrong answer.
Units, Assumptions and the Limits of the Model
The calculation assumes ideal conditions: no air resistance, no heat loss, and dimensions that do not change while you work. Those assumptions are reasonable for most classroom and engineering estimates, and unreasonable for anything more precise.
Where a value is a rate, it has to be quoted for the same period as everything else. A per-hour figure cannot be combined with a per-day figure without converting one of them first.
A Worked Example
Working through an example, with elasticity module (m) set to 10, number of active coils (na) set to 5, achieved torsion angle (α) set to 2, the calculator returns wire diameter (d) of 0.09901, and mean diameter (d) of 9.90099, and free length for plain ends of 25.09901. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out force applied to the spring (f)?
Enter elasticity module (m), number of active coils (na), achieved torsion angle (α), number of body coils (nb), extension/compression δx, distance of lever arm (r), length, first end (l1), length, second end (l2), outer diameter (od), pitch, modulus of rigidity (g) and spring index c. The calculator then works through the relationship and reports force applied to the spring (f), free length for squared and ground end and torque applied to the spring (m).
What does the spring actually calculate?
It takes elasticity module (m), number of active coils (na), achieved torsion angle (α), number of body coils (nb), extension/compression δx, distance of lever arm (r), length, first end (l1), length, second end (l2), outer diameter (od), pitch, modulus of rigidity (g) and spring index c and converts them into force applied to the spring (f), free length for squared and ground end and torque applied to the spring (m) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter elasticity module (m)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.