Hooke’s Law Spring Restoring Force, Potential Energy & Frequency Calculator

Evaluate linear spring force, stored elastic joules, and natural frequency.

Spring Restoring Force (F = kx)
119 N
Stored Elastic Potential Energy 8.33 J
Harmonic Natural Frequency 2.93 Hz
Oscillation Period 0.34 s
Inputs
N/m
Spring stiffness constant (k) in Newtons per meter.
m
Spring compression or extension distance (x) in meters.
kg
Mass attached to the spring in kilograms.
Results & Graph
Spring Restoring Force (F = kx)
119 N
Stored Elastic Potential Energy
8.33 J
Harmonic Natural Frequency
2.93 Hz
Oscillation Period
0.34 s

Spring Restoring Force (F = kx)

Graph 1 • Spring Constant N Per M Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 N 96.4 N 192.8 N 50%: 59.5 N 59.5 50% 75%: 89.25 N 89.3 75% 100%: 119 N 119 100% 125%: 148.75 N 148.8 125% 150%: 178.5 N 178.5 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Spring Restoring Force (F = kx) 119 N Stored Elastic Potential Energy 8.33 J Harmonic Natural Frequency 2.93 Hz Oscillation Period 0.34 s
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Spring Restoring Force (F = kx)119 NStored Elastic Potential Energy8.33 JHarmonic Natural Frequency2.93 HzOscillation Period0.34 s
Summary: Deflecting an 850 N/m spring by 0.14 m exerts 119 N of restoring force and stores 8.33 J of elastic potential energy.
Summary: Deflecting an 850 N/m spring by 0.14 m exerts 119 N of restoring force and stores 8.33 J of elastic potential energy.
⚡ Send result to: Scientific →Ohm's Law & Voltage Drop →Molarity, HP & Dew Point →
Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Hooke’s Law Spring Physics & Engineering Equation

F = k × x
Uelastic = 0.5 × k × x²
f = (1 / 2π) × k / m
F = k × x; U_elastic = 0.5 × k × x²; f = (1 / 2π) × √(k / m)
  • springConstantNPerM: Spring Constant N Per M (N/m)
  • displacementM: Displacement M (m)
  • attachedMassKg: Attached Mass Kg (kg)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Hooke’s Law Spring

Evaluate linear spring force, stored elastic joules, and natural frequency.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: F = k × x; U_elastic = 0.5 × k × x²; f = (1 / 2π) × √(k / m).
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Hooke’s Law Spring via F = k × x; U_elastic = 0.5 × k × x²; f = (1 / 2π) × √(k / m).

Frequently Asked Questions

What equation powers the Hooke’s Law Spring Restoring Force, Potential Energy & Frequency Calculator?

It evaluates F = k × x; U_elastic = 0.5 × k × x²; f = (1 / 2π) × √(k / m) using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Classical Mechanics & Kinematics

Hooke’s Law Spring Restoring Force, Potential Energy & Frequency Calculator: inputs, method, and how to read the result

Evaluate linear spring force, stored elastic joules, and natural frequency.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Spring Constant N Per M: Spring stiffness constant (k) in Newtons per meter.
  • Displacement M: Spring compression or extension distance (x) in meters.
  • Attached Mass Kg: Mass attached to the spring in kilograms.

What the calculation includes

With the default values shown, Spring Restoring Force (F = kx) is 119 N. The calculation follows Hooke’s Law Spring Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Spring Constant N Per M from 850 N/m to 935 N/m changes Spring Restoring Force (F = kx) from 119 N to 130.9 N. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Science & Engineering: Scientific Calculator, Ohm's Law, Wire Voltage Drop & Resistor Series/Parallel Calculator, Molarity, Density, Engine Horsepower & Dew Point / Weather Calculator.