Type a line (spring wire 4 mm OD 32 mm 8 active coils free length 70 mm fitted 55 mm) or fill in the fields: the line and the fields stay in step.
Enter the wire diameter, the outside diameter and the active coils of a helical compression spring, or the total coils with the ends, and the calculator gives the spring rate in N/mm and lbf/in, the mean diameter and the spring index. With the free length and the fitted length it gives the load at the fitted length in N, kgf and lbf, and with a load the deflection. It shows the working with your numbers, draws the spring free and as fitted, and gives a line you can copy or add to a request.
It is meant for relief and safety valve springs, check valve, governor and fuel valve springs: measure the old spring on board, then the replacement, and compare the rate and the load at the fitted length. The figures are for that comparison only: there is no stress, fatigue or buckling check here and no material advice. For hard-drawn steel wire (ASTM A227) G is taken as 79.3 GPa, a typical value to check against the material sheet; for other wire, enter G from the sheet.
The rate k = G x d^4 / (8 x D^3 x n): d the wire diameter, D the mean diameter, n the active coils, G the shear modulus. Wire 4 mm, mean diameter 28 mm, 8 active coils, G 79 300 N/mm2: k = 20 300 800 / 1 404 928 = 14.45 N/mm. The wire counts to the fourth power, so measure it carefully.
The mean diameter is to the centreline of the wire: D = OD - d = ID + d, which is 28 mm for a 32 mm outside diameter and 4 mm wire. The end coils that sit on the seats do not work: with closed ends there are two active coils fewer than the total, with plain and ground ends one fewer.
The deflection as fitted is s = free length - fitted length, and the load F = k x s. Free length 70 mm, fitted length 55 mm: s = 15 mm, F = 14.45 x 15 = 216.7 N, or 22.1 kgf. A replacement with the same rate and the same free length gives the same load as fitted.
| Quantity | Relation | Note |
|---|---|---|
| Spring rate | k = G x d^4 / (8 x D^3 x n) | N/mm with d and D in mm and G in N/mm2 |
| Mean diameter | D = OD - d = ID + d | to the centreline of the wire |
| Active coils | n = total - 2 (closed ends, ground or not); total - 1 (plain and ground ends); n = total (plain ends) | the end coils that sit on the seats do not work |
| Load | F = k x s; s = free length - fitted length | N; 1 kgf = 9.80665 N; 1 lbf = 4.44822 N |
| Deflection at a load | s = F / k | mm |
| Spring index | C = D / d | a figure for comparing, with no recommended range |
| Shear modulus | G = 79.3 GPa (hard-drawn steel wire, ASTM A227) | typical value: check the material sheet; for other wire grades the published values differ |
| Units | 1 in = 25.4 mm; 1 lbf/in = 0.175127 N/mm | 1 GPa = 1000 N/mm2 |
The rate formula is for a helical compression spring of round wire; the active coils are counted from the ends of the spring. The shear modulus for hard-drawn steel wire (ASTM A227) is a typical value; for other materials G comes from the material sheet.
The rate k = G d^4 / (8 D^3 n), the relation of the mean diameter to the outside and inside diameters and the active coils for each type of end come from independent engineering references on spring design that give them the same way; the working is checked against two published worked examples. The references give different recommended ranges for the spring index, so the calculator shows the index as a figure only. For the shear modulus, the material tables of two spring makers and an engineering reference give the same 11.5 x 10^6 psi (79.3 GPa) for hard-drawn steel wire (ASTM A227), so that is the one preset, marked as a typical value; for music wire, oil-tempered wire, stainless steel and bronze there is no preset.
From k = G d^4 / (8 D^3 n): d the wire diameter, D the mean coil diameter, n the active coils and G the shear modulus of the wire. With d and D in mm and G in N/mm2, k comes out in N/mm. Wire 4 mm, outside diameter 32 mm, 8 active coils, G 79.3 GPa (79 300 N/mm2): D = 32 - 4 = 28 mm, and k = 79 300 x 4^4 / (8 x 28^3 x 8) = 20 300 800 / 1 404 928 = 14.45 N/mm, or 82.51 lbf/in. The wire counts to the fourth power and the diameter to the third, so a small change in either moves the rate a lot.
The formula works on the centreline of the wire, so it takes the mean coil diameter: D = OD - d, or ID + d. On board the outside diameter is the one measured across the coils, and the calculator takes the wire off it. Putting the outside diameter in place of the mean one gives a wrong rate: for the 4 mm wire and 32 mm outside diameter above, 9.68 N/mm instead of 14.45 N/mm, a third too low.
Only the coils free to move work; the end coils that sit on the seats do not. With closed (squared) ends, ground or not, the active coils are the total less two; with plain and ground ends, the total less one; with plain ends, all the coils. A spring with 10 coils in all and closed and ground ends has 8 active coils. Count the total on the old spring and write the ends, or give the active coils directly.
The deflection is the free length less the fitted length, s = L0 - L1, and the load is F = k s. The spring above with a free length of 70 mm fitted at 55 mm: s = 15 mm and F = 14.45 x 15 = 216.7 N, which is 22.1 kgf or 48.7 lbf. Given a load instead, the calculator gives the deflection s = F / k and the length of the spring under that load.
Unless G is entered, 79.3 GPa (11.5 x 10^6 psi): the typical value that spring material tables give for hard-drawn steel wire (ASTM A227), so check the material sheet. The rate moves in step with G: a G 2 % higher gives a rate 2 % higher. There is no preset for music wire, oil-tempered wire, stainless steel, bronze or alloy wire: enter G from the material sheet for those.
The wire diameter, the outside diameter (or the mean D or the inside diameter) and the coils, active or total with the ends; the free length and the fitted length, or a deflection or a load; G if the wire is not hard-drawn steel (ASTM A227); and a measured rate if there is one. Lengths in mm or inches, loads in N, kN, kgf or lbf, rates in N/mm or lbf/in. There is no stress, fatigue or buckling check and no material advice: the figures are for comparing a replacement with the old spring.
The calculator gives the rate and the loads of a spring from its sizes. When a replacement spring is needed, send the line from the calculator with the details of the valve or the unit, a photograph of the nameplate and the drawing or the part number, and Vessel Core checks the details before an offer goes back.
