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Physics Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

SHM Energy Calculator

You can calculate the total, kinetic and potential energy of a spring oscillator at any displacement, plus its speed, angular frequency and period, with the KE/PE split shown at that point.

Runs in your browserFree · No sign-up · No watermark
m, k, A, x → ERuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
m, k, A, x → E
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Physics Tools

About SHM Energy Calculator

In an undamped spring oscillator, energy moves between the spring and the moving mass, but the total stays constant. At maximum displacement all of the energy is potential, and through equilibrium all of it is kinetic; the oscillation simply exchanges one form for the other.

This calculator applies E = ½kA², PE = ½kx² and KE = E − PE to find the energy split at any displacement within the amplitude. It also reports the speed from v = ω√(A² − x²), the angular frequency ω = √(k/m) and the period, so the state is fully described.

What this tool does

The details that matter when you use SHM Energy Calculator for real work.

  • Total, kinetic and potential energy

    The three energies are reported together, with the split at the chosen displacement.

  • KE/PE split at x

    Percentages and proportional bars show how the total energy is divided at the current position.

  • Speed at displacement

    Speed follows v = ω√(A² − x²), reaching its maximum at equilibrium and zero at the amplitude.

  • Angular frequency and period

    ω = √(k/m) and T = 2π/ω are reported, so the oscillator's timing is available with its energy.

  • Unit choices

    Mass can be entered in kilograms or grams, and amplitude and displacement in meters or centimeters.

  • Formula steps

    The energy and speed equations are printed with the substituted values for checking.

How to use SHM Energy Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Enter the oscillator properties

    Set the mass in kg or g and the spring stiffness in N/m.

  2. 02

    Set the amplitude

    Enter the maximum displacement A in meters or centimeters.

  3. 03

    Set the current displacement

    Enter x within the amplitude; the tool reports the energy split at that position.

  4. 04

    Read the energies and speed

    The headline shows total energy, and the cards give kinetic and potential energy, speed, angular frequency and period.

  5. 05

    Check the working

    The formula panel shows E = ½kA², PE = ½kx² and the speed equation with the values substituted.

How this tool works

Works with
m, k, A, x → E
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Models the undamped spring oscillator only; damping, driving and pendulum energy are not included.
  • Assumes a linear spring obeying Hooke's law with no mass or internal losses.
  • The energy values are ideal-model results; real springs lose energy to internal friction.

Privacy and file handling

Mass, stiffness, amplitude and displacement are processed entirely in your browser. Nothing is uploaded, stored or logged, and no network request is made.

Read the full privacy policy

SHM Energy Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is the total energy of a spring oscillator?
The total mechanical energy is E = ½kA², where k is the spring stiffness and A is the amplitude. In the undamped model it stays constant while the mass oscillates, with the energy trading between potential and kinetic forms.
Where is the kinetic energy maximum in simple harmonic motion?
Kinetic energy is maximum at the equilibrium position x = 0, where the potential energy is zero and the speed is ωA. Moving away from equilibrium converts kinetic energy into spring potential energy, so the speed falls toward the amplitude.
Where is the potential energy maximum?
Potential energy is maximum at the extremes of the motion, where |x| = A. At that point the speed is zero and all of the oscillator's energy is stored in the spring, so PE equals the total energy ½kA².
How does the speed depend on displacement?
The speed is v = ω√(A² − x²), which is why it is largest at x = 0 and zero at |x| = A. Substituting x = 0 gives the maximum speed ωA, while substituting x = ±A gives zero, consistent with the turning points.
Does the period of the oscillator depend on the amplitude?
No, not in the ideal simple-harmonic model: T = 2π√(m/k) depends only on the mass and stiffness. A larger amplitude increases the energy and maximum speed, but the time for one full cycle stays the same.
What happens to the energy if there is damping?
The total energy decreases over time as damping removes mechanical energy, and the oscillation amplitude shrinks. That is outside this calculator's model, which assumes an ideal undamped spring where total energy is conserved.
Can the calculator describe a pendulum's energy?
No, this tool models the spring oscillator. A pendulum exchanges kinetic energy with gravitational potential energy mgh relative to its lowest point, and its energy expression uses height rather than spring compression.
What units does the energy calculator use internally?
Mass is converted to kilograms, stiffness stays in newtons per meter, and lengths are converted to meters before any formula runs. The reported energies are in joules, and the speed is in meters per second.

Background reading

Format guides that explain the trade-offs behind SHM Energy Calculator.