Potential Energy vs Kinetic Energy: Which Page?

This comparison page maps given variables → DevOkk tool → formula, separates PE = mgh from KE = ½mv², connects conservation problems, and notes when power belongs. Tools: Potential Energy Calculator, Kinetic Energy Calculator, Power Calculator, Physics Calculators hub. No account.

Cross-links: Force, pressure, kinetic energy: which calculator, How to calculate potential energy, How to calculate kinetic energy, How to calculate power.

Stored versus motion in one sentence each

Gravitational potential energy (PE) - energy from vertical position in uniform g: PE = mgh, joules.

Kinetic energy (KE) - energy of translational motion: KE = ½mv², joules.

Both are scalars in joules. Height h signals PE (with mass). Speed v signals KE (with mass). Problems with both often use conservation: PE_initial + KE_initial = PE_final + KE_final (ideal case).

The comparison table is the routing chart

Given	Open	Formula
m and h	Potential energy calculator	PE = mgh
m and v	Kinetic energy calculator	KE = ½mv²
Drop height, find v	PE then KE (or v = √(2gh))	mgh = ½mv²
Spring k and x	½kx² on paper	Not mgh
Energy and time	Power calculator	P = E/t
Mixed worksheet	Physics calculators	Route first

Circle h or v before clicking.

Potential energy: PE = mgh

Near Earth’s surface:

PE = m g h

• m in kg
• g ≈ 9.8 m/s² unless given otherwise
• h in m (vertical height relative to your chosen zero)

Example: m = 2.0 kg, h = 1.5 m, g = 9.8 m/s²
PE = 2.0 × 9.8 × 1.5 = 29 J

Open Potential Energy Calculator when height and mass define the state-not speed.

Zero of height: PE = 0 anywhere you define. Only differences matter in ΔPE = mgΔh. A crate on a table can have PE = 0 on the table and negative PE relative to the floor-that is bookkeeping.

Not KE: If the problem gives speed at the top of a ramp, you may need KE there and PE if height is nonzero.

Full guide: How to calculate potential energy.

Kinetic energy: KE = ½mv²

KE = ½ m v²

• m in kg
• v in m/s (speed; v² removes direction)

Example: m = 0.145 kg (baseball), v = 40 m/s
KE = 0.5 × 0.145 × 1600 = 116 J

Doubling speed quadruples KE.

Open Kinetic Energy Calculator when mass and speed appear without asking for stored height energy.

Not PE = mgh: Acceleration alone does not enter KE unless you first find v from kinematics.

km/h trap: Convert to m/s before squaring. 72 km/h = 20 m/s.

Full guide: How to calculate kinetic energy.

Conservation: one problem, two tools

Classic drop (no air resistance): Object released from rest at height h. Find v just before impact.

At top: PE = mgh, KE = 0
At bottom: PE = 0 (floor as zero), KE = ½mv²

mgh = ½mv² → v = √(2gh)

Mass cancels. m = 3 kg or 300 kg-same v if only height drives the motion.

Workflow:

1. Confirm frictionless wording.
2. Optional: Potential Energy Calculator for PE at top = mgh.
3. Set KE = that value and solve for v, or use Kinetic Energy Calculator with KE filled from mgh.

Example: h = 5.0 m, g = 9.8 m/s²
v = √(2 × 9.8 × 5) = √98 ≈ 9.9 m/s

With initial speed: At top, KE₀ = ½mv₀² and PE₀ = mgh. At bottom, ½mv² = mgh + ½mv₀². Use both tools or algebra; do not assume v = √(2gh) alone.

When neither pure PE nor pure KE is enough

Ramp with friction: Energy not conserved fully-thermal loss. You may need work by friction = f × d from force concepts. See Force, pressure, kinetic energy for F = ma lane.

Pendulum: At highest point, v = 0, PE max. At bottom, PE min, KE max. Same mgh ↔ ½mv² swap with h as vertical rise, not string length along the arc.

Springs: Elastic PE = ½kx², not mgh. A compressed spring problem belongs in elastic PE, not the gravitational Potential Energy Calculator unless the spring also lifts a mass vertically.

Orbits: U = −GMm/r replaces mgh. Intro worksheets with “height on a lab bench” stay in mgh.

Power: after you have joules

Power is not potential or kinetic energy. It is rate:

P = E / t (watts = joules per second)

Use Power Calculator when:

• A motor lifts mass m through h in time t → E ≈ mgh → P = E/t
• A car’s KE changes by ΔKE in time t → P = ΔKE/t (average)

Example: 600 J of PE gained in 4 s during a slow lift
P = 600/4 = 150 W

Do not confuse pressure P = F/A (pascals) with power P = E/t (watts). Units disambiguate.

Electrical power P = VI is another branch-power guide.

Unit traps

Mistake	Effect
m in grams	J off by 1000×
h in cm	PE off by 10⁴×
v in km/h squared	KE wrong
Using weight (N) as m	Both formulas wrong
Horizontal distance as h on ramp	Use vertical component

SI checklist: kg, m, m/s, J.

Worked examples by tool

PE example

A 45 kg student on a 2.0 m diving platform (platform as reference for h).

PE = 45 × 9.8 × 2.0 = 882 J
Tool: Potential Energy Calculator.

KE example

Same student hits water at 6.0 m/s (given).

KE = 0.5 × 45 × 36 = 810 J
Tool: Kinetic Energy Calculator.

Real dive loses energy to air drag-882 J and 810 J not matching hints at non-ideal physics.

Conservation example

Ball dropped from 3.2 m, g = 9.8, find v.

v = √(2gh) = √(62.72) ≈ 7.9 m/s
Tools: PE at top for check; KE with that v for check.

Power example

Crane lifts 500 kg by 12 m in 20 s.

E ≈ mgh = 500 × 9.8 × 12 = 58,800 J
P = 58,800/20 = 2940 W ≈ 2.9 kW
Tools: Potential Energy Calculator then Power Calculator.

When to use the physics-calculators hub

Open Physics Calculators when:

• The worksheet header says “Energy” without mgh or ½mv²
• A problem chain goes PE → KE → power
• Force and pressure appear on the same page as energy

The hub routes; it does not replace reading h versus v.

Homework workflow

Step 1 - Underline givens: h, v, m, t, k, x.

Step 2 - Match table: height → PE; speed → KE; time after energy → power.

Step 3 - Convert units: g→kg, cm→m, km/h→m/s.

Step 4 - One primary tool per sub-question.

Step 5 - Conservation check: PE lost ≈ KE gained if frictionless.

Step 6 - Sanity check: Double v → quadruple KE; double h → double PE.

Energy bar charts on paper

Many courses ask for a bar chart of PE and KE at two instants. Label axes in joules.

Example - pendulum bob at extremes and bottom:

At left extreme: PE = mgh_max, KE = 0
At bottom: PE = 0 (if lowest point is zero), KE = mgh_max

The bars swap height; total mechanical energy bar stays level if frictionless.

Drawing the chart before opening calculators catches sign errors on PE when the zero is mid-swing.

Relative motion and reference frames

PE depends on vertical h in your chosen frame, not on whether the observer moves. A ball in a moving train still has mgh relative to the train floor. KE uses speed relative to the same frame as the KE question-usually the ground for a runner, the train for a passenger juggling.

If two frames appear in one problem, convert v before KE; do not mix ground height with train-relative speed without transformation.

Intro versus AP depth

AP problems may combine rotational KE (½Iω²) with translational ½mv². DevOkk’s Kinetic Energy Calculator targets translational ½mv² unless the page documents otherwise. If I and ω appear, that is a different formula lane-still joules, but not the same input form.

Gravitational PE at large altitude may need g(h) variation; benchtop labs stay at mgh.

Privacy

Calculators run locally. No account. Show mgh or ½mv² on paper if method is graded.

The routing habit

Height and mass → Potential Energy Calculator (PE = mgh). Speed and mass → Kinetic Energy Calculator (KE = ½mv²). Drop problems → equate mgh and ½mv². Energy over time → Power Calculator. Mixed lanes → Physics Calculators. Pair with potential energy and kinetic energy guides for zeros, ramps, and significant figures.