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In this article, you will learn a complete overview of the spring constant such as its definition, formula, unit, dimensional formula, affecting factor, calculation, and many more.So, without wasting time lets get started.Spring Constant is the restoring force exerted by spring to restore the position against a unit displacement caused by an external force. The higher the value of the spring constant higher will be the stiffness of the spring which means a higher load will be required to compress or deflect a spring.It is also called spring rate and stiffness constant. It is always a positive or a non-zero value.According to Hookes Law,Force is directly proportional to the deflection or displacement of the spring.Mathematically,F ∝ xF = K.x Where K is a spring constant.The restoring force (F) developed in spring works opposite to the force applied.So,Fr = - FFr = - K.xWhich can also be written as, K = - (Frx)or K = FxWhere,Fr = Restoring force in spring (N)x = Deformation or displacement in spring (m)F = Force applied to springK = Spring ConstantSpring rate refers to the amount of force required to compress or extend or twist a spring by unit displacement or deflection.Spring rate does not primarily depend on the material grade of spring.Putting the values in the formula derived from Hookes Law,K = Fx = (W2 - W1)(h2 - h1)Formula for calculating spring constant K = (G × d⁴)(8 × Dm³ × Nac)Where, G - Modulus of Rigidity d - Wire Diameter Dm- Mean Diameter of SpringNac- No. of Active CoilsAs we know the unit of force and distance in the SI system are Newton (N) and Metre (M) respectively.So,Spring Constant,K = FxK = NmHence in the SI system, the unit of the spring constant will be Nm.As we know the unit of force and distance in the SI system are Pound (Ib) and Feet (ft) respectively.So,Spring Constant,K = FxK = IbftHence in the FPS system, the unit of the spring constant will be Ibft.As we know,K = FxSince,Force = mass (m) × acceleration (a)Hence,K = (m × a)x As we know the unit of mass and acceleration are kg and ms² respectively.So,K = kg × m s ⁻²mK = M T⁻²Hence the dimensional formula for spring constant K will be M T⁻².Show in the figure combination of spring in series and parallel which are described below in detail.In series combinations, tension is the same in all the springs & extensions will be different. ( If k is the same then deformation is also the same ).In a series combination, an extension of springs will be reciprocal of its spring constant.The total displacement when the spring is in series,x = x₁ + x₂As we know spring ConstantF = K × xSo,FK = xHence,FKeq = FK₁ + FK₂So, the equivalent constant in the series combination Keq is given by : 1Keq = 1 K₁ + 1 K₂ In parallel combination, extension is the same for both springs but force acting will be different.If the force acting in the spring is F then the total force acting on the spring,F = F₁ + F₂ As we know,F = K × xSo,F = ( K₁x + K₂ x ) F = ( K₁ + K₂ )x K × x = ( K₁ + K₂ )x So, the equivalent constant in parallel combination Keq is given by : Keq = K₁ + K₂The spring constant of a spring depends on the following factorsWire Diameter of Spring Modulus of RigidityCoil DiameterNo. of Active or Effective Coils If the diameter of the spring wire is increased, the spring constant will increase.If the modulus of rigidity of the spring material is increased, the spring constant will increase.If the diameter of the spring coil is increased, the spring constant will decrease.If the number of coils of the spring is increased, the spring constant will decrease.See Also:What is Body Mass IndexParallel Axis TheoremModulus of ElasticityModulus of Resilience Bending StressWhat is the spring constant if it takes 30 N to stretch a spring 0.2 m?SolutionGiven Data,F = 30 Nx = 0.2 mK =?As we know,F = K × xSo,K = FxK = 300.2K = 150 NmA spring of force constant k is cut into lengths of ratio 1: 2 : 3 . They are connected in series and the new force constant is Ks. Then they are connected in parallel and the force constant is Kp. Then what is the ratio of Ks:Kp?SolutionAs we know,K ∝ (1l)So,K₁l₁ = ConstantHere K is the spring constant and l is the spring length So in Series combination,1Ks = 1 K₁ + 1 K₂ + 1K₃1Ks = 1 + 2 + 31Ks = 6Ks = 16Now in parallel combination,Kp = K₁ + K₂ + K₃Kp = 1 + 12 + 13Kp = 116The ratio of the Series and Parallel combination of the spring will be,Ks:Kp = 1:11So here you have to know all aspects related to the spring constant. If you have any doubt then you are free to ask me by mail or on the contact us page.Thank You. This tool converts Spring constant Units. It also includes below conversion tables. Metric systemNm : newton per meterNcm : newton per centimeterNmm : newton per millimeterUS-UK Customarylbfin : pound force per inchSpring constant Unit Conversion TablesMetric system Metric system # Nm Ncm Nmm 1 Nm = 10.010.001 1 Ncm = 10010.1 1 Nmm = Metric system US-UK Customary # lbfin 1 Nm = 0.0057 1 Ncm = 0.571 1 Nmm = 5.7101 US-UK Customary Metric system # Nm Ncm Nmm 1 lbfin = 175.12681.75130.1751 See alsoUnit conversion
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