How this instrument works
A pendulum bob does not carry one energy value for the whole swing — it carries a different kinetic energy at every point along the arc, and this instrument answers for exactly one of those points. Feed it the bob's mass and its speed at the instant you care about, and KE = ½mv² returns the energy of motion right there. The formula treats the two inputs asymmetrically: mass sets the result in direct proportion, but speed is squared, so a bob moving twice as fast at some point carries four times the kinetic energy at that same point, not twice.
Inside a real swing, this number rises and falls on a fixed schedule set by height, not by the clock. Release the bob from rest at the top of its arc and its kinetic energy there is zero; as it drops, gravitational potential energy converts over instant by instant, until the bob crosses the lowest point of the swing carrying the maximum speed — and therefore the maximum kinetic energy — of the entire cycle. Past that low point the exchange runs in reverse, energy draining back into height as the bob climbs toward the far side, reaching zero again at the opposite turning point before falling back.
Where the speed itself comes from matters more here than in most kinetic-energy problems, because a swinging bob is rarely clocked with a stopwatch — a photogate timing a flag through the beam at the bottom of the arc, or a motion sensor tracking the string, is the usual source, and that reading only holds good for the instant it was taken. The formula also assumes a point mass in pure translation: a bob with real size, or a rigid rod standing in for a string, carries additional rotational kinetic energy about the pivot that ½mv² alone does not capture — the domain of a physical-pendulum treatment, not this one. The same relationship, applied the same way, is what a Charpy impact tester relies on: its hammer is released from a fixed height so it always strikes a test specimen with a known, repeatable kinetic energy at the bottom of its arc.
- Enter the Pendulum bob mass — grams or kilograms — the default 0.5 kg matches a typical lab bob.
- Enter Speed at this point in the swing: the bob's tangential speed at the instant you're checking, in m/s or ft/s, not an angle or a position.
- Read Kinetic energy at this point in joules, or switch its unit to kilojoules for a heavier hammer or flywheel.
- Move the instant you're checking — the bottom of the arc for the peak reading, either extreme for zero — and re-enter Speed at this point in the swing to see the value change.
- Know the release height instead of the speed? Convert it first with v = √(2gh), then enter that figure as Speed at this point in the swing.
Worked example — a 0.5 kg bob at the bottom of its swing
Set Pendulum bob mass to 0.5 kg and Speed at this point in the swing to 2 m/s — the bob crossing the lowest point of its arc, where the swing runs fastest. Square the speed first: 2² = 4 m²/s². Multiply by the mass and halve the result: KE = 0.5 × 0.5 × 4 = 1.0 J. That one joule is the largest kinetic energy this particular pendulum reaches anywhere in its swing, because nowhere else in the arc is it moving this fast.
At the top of the same swing, an instant later in the cycle, Speed at this point in the swing drops to 0 m/s and Kinetic energy at this point reads 0 J — all of that one joule has gone back into height. Energy conservation ties the two readings together: mgh at the release point equals ½mv² at the bottom, so this bob's 1.0 J corresponds to a drop of about 0.204 m, just over 20 cm, above the low point of the arc.
Questions
Why does the kinetic energy change throughout a pendulum's swing?
Because speed itself changes throughout the swing. Kinetic energy depends on speed, so as the bob trades height for speed on the way down and speed for height on the way back up, KE rises to a maximum at the lowest point of the arc and falls to zero at both turning points, where the bob is momentarily motionless before reversing direction.
Where should I measure the speed for this calculator?
At whatever point in the swing you want the energy for — but the bottom of the arc is usually easiest, since that is both the fastest point and the one a photogate or motion sensor can catch cleanly as the bob crosses it. Enter that reading as Speed at this point in the swing and the result is the energy at that instant only.
How is this different from a pendulum's period calculation?
Period depends only on the pendulum's length and gravity — mass and speed never enter it. Kinetic energy at a point in the swing is the opposite: it depends entirely on mass and instantaneous speed, and length never enters this formula directly. The two calculators answer different questions about the same swinging bob.
Can I get the speed from the release height instead of measuring it directly?
Yes, if losses to air drag and pivot friction are small. Energy conservation gives v = √(2gh) for a drop of height h above the point you're checking, so a bob released 0.204 m above its lowest point arrives there at 2 m/s — the exact speed behind this page's own worked example.
Does the pendulum's length or swing angle affect the kinetic energy?
Not directly. Once you know the mass and the speed at a point, KE = ½mv² needs nothing else — length and release angle only matter earlier, in setting what that speed actually is at each point in the arc. A longer pendulum released from the same angle crosses its lowest point more slowly than a shorter one, which changes the kinetic energy only indirectly, through v.
Is any rotational energy in the bob or string included in this result?
No. This formula treats the bob as a single point mass moving in pure translation. A bob large enough to spin, or a rigid rod substituting for a string, also stores rotational kinetic energy about the pivot, ½Iω², which this instrument does not add — that case calls for a physical-pendulum or rotational-kinetic-energy treatment instead.