Energy Calculator

Calculate different types of mechanical energy

Kinetic Energy (KE = 0.5mv²)

Mass (kg):

Velocity (m/s):

Gravitational Potential Energy (PE = mgh)

Height (m):

Gravity (m/s²):

Elastic Potential Energy (PE = 0.5kx²)

Spring Constant (N/m):

Displacement (m):

Energy from Power (E = Pt)

Power (W):

Time (s):

Energy Formulas

Kinetic Energy: KE = (1/2) * m * v²

Gravitational PE: PE = m * g * h

Elastic PE: PE = (1/2) * k * x²

Work-Energy: E = P * t

What is Energy?

Energy is the capacity to do work or cause change. It's one of the most fundamental concepts in physics and exists in many forms that can be converted from one to another.

Energy Form	Description	Example
Kinetic	Energy of motion	Moving car, flying ball
Potential (gravitational)	Stored energy due to position	Rock on cliff, raised weight
Potential (elastic)	Stored in deformed objects	Compressed spring, stretched rubber band
Thermal	Internal energy from particle motion	Hot coffee, steam
Chemical	Stored in molecular bonds	Food, batteries, fuel
Electrical	From electric charge movement	Lightning, circuits
Nuclear	Stored in atomic nuclei	Nuclear reactor, sun

The SI unit of energy is the Joule (J), equal to 1 kg·m²/s² or 1 N·m.

Energy Unit Definition

1 Joule = 1 N·m = 1 kg·m²/s²

Where:

J= Joule, SI unit of energy
N·m= Newton-meter (force × distance)
kg·m²/s²= Base SI units

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion:

Relationship	Implication	Example
KE ∝ m	Double mass = double KE	Truck vs car at same speed
KE ∝ v²	Double speed = 4× KE	Car at 60 mph vs 30 mph
KE = ½mv²	Mass and velocity both matter	Bullet vs baseball

Object	Typical KE	Context
Walking person (70 kg, 1.4 m/s)	69 J	Casual walking
Thrown baseball (0.145 kg, 40 m/s)	116 J	Professional pitch
Car (1500 kg, 30 m/s)	675,000 J	Highway speed (~108 km/h)
Commercial aircraft	~3 billion J	At cruising speed

Kinetic Energy Formula

KE = ½mv²

Where:

KE= Kinetic energy (Joules)
m= Mass (kg)
v= Velocity (m/s)

Potential Energy

Potential energy is stored energy due to an object's position or configuration:

Type	Formula	Depends On	Example
Gravitational PE	PE = mgh	Mass, height, gravity	Water behind dam
Elastic PE	PE = ½kx²	Spring constant, compression	Compressed spring
Electric PE	PE = kq₁q₂/r	Charges, distance	Charged particles
Chemical PE	Varies by bonds	Molecular structure	Gasoline, food

Reference point: Potential energy is always measured relative to a reference point. Ground level is often chosen as h = 0 for gravitational PE.

Gravitational Potential Energy

PE = mgh

Where:

PE= Potential energy (J)
m= Mass (kg)
g= Gravitational acceleration (9.81 m/s²)
h= Height above reference (m)

Work-Energy Theorem

The work-energy theorem connects work and kinetic energy:

Concept	Formula	Meaning
Work done	W = Fd cos(θ)	Force × displacement × cos(angle)
Work-energy theorem	W_net = ΔKE	Net work equals KE change
Positive work	W > 0	Increases KE (speeds up)
Negative work	W < 0	Decreases KE (slows down)

Application: When calculating how much energy is needed to accelerate an object, use W = ΔKE = ½mv_f² - ½mv_i²

Work-Energy Theorem

W_net = ΔKE = ½mv_f² - ½mv_i²

Where:

W_net= Net work done (J)
ΔKE= Change in kinetic energy
v_f, v_i= Final and initial velocities

Conservation of Energy

The Law of Conservation of Energy states that energy cannot be created or destroyed, only converted:

Scenario	Energy Conversion	Equation
Falling object	PE → KE	mgh = ½mv²
Thrown ball rising	KE → PE	½mv² = mgh
Pendulum	PE ↔ KE (cyclic)	E_total = constant
Roller coaster	PE ↔ KE with friction loss	E_mech - E_friction = E_final

Mechanical energy: E_mech = KE + PE. In absence of friction, mechanical energy is conserved.

Conservation of Mechanical Energy

KE₁ + PE₁ = KE₂ + PE₂ ½mv₁² + mgh₁ = ½mv₂² + mgh₂

Where:

KE + PE= Total mechanical energy
Subscripts 1, 2= Initial and final states

Energy Units and Conversions

Energy is measured in various units depending on the application:

Unit	Symbol	Equivalent in Joules	Common Use
Joule	J	1	Physics, SI standard
Calorie	cal	4.184	Chemistry, older nutrition
Kilocalorie	kcal (Cal)	4,184	Food nutrition labels
Kilowatt-hour	kWh	3,600,000	Electricity billing
Electron-volt	eV	1.602 × 10⁻¹⁹	Particle physics
British thermal unit	BTU	1,055	HVAC, heating
Foot-pound	ft·lb	1.356	Engineering (US)

Note: The "Calorie" on food labels (capital C) is actually a kilocalorie (1000 calories).

Mass-Energy Equivalence

Einstein's famous equation relates mass and energy:

Concept	Value	Implication
Speed of light (c)	299,792,458 m/s	c² = 9 × 10¹⁶ m²/s²
1 kg of mass	9 × 10¹⁶ J	~21 megatons TNT equivalent
1 gram of mass	9 × 10¹³ J	~21 kilotons TNT
Nuclear fission efficiency	~0.1% mass converted	Still enormous energy

In practice: Nuclear reactions convert a tiny fraction of mass to energy, but c² is so large that the energy released is enormous.

Mass-Energy Equivalence

E = mc²

Where:

E= Energy (Joules)
m= Mass (kg)
c= Speed of light (299,792,458 m/s)

Worked Examples

Kinetic Energy of a Vehicle

Problem:

A 1,200 kg car is traveling at 25 m/s (90 km/h). Calculate its kinetic energy.

Solution Steps:

1Identify values: m = 1,200 kg, v = 25 m/s
2Apply KE formula: KE = ½mv²
3Substitute: KE = ½ × 1,200 × 25²
4Calculate: KE = ½ × 1,200 × 625 = 375,000 J
5Express in kJ: KE = 375 kJ

Result:

Kinetic energy = 375,000 J (375 kJ)

Potential Energy at Height

Problem:

A 50 kg object is lifted to a height of 20 meters. What is its gravitational potential energy?

Solution Steps:

1Given: m = 50 kg, g = 9.81 m/s², h = 20 m
2Apply PE formula: PE = mgh
3Substitute: PE = 50 × 9.81 × 20
4Calculate: PE = 9,810 J

Result:

Potential energy = 9,810 J (≈ 9.81 kJ)

Conservation of Energy - Falling Object

Problem:

A 2 kg ball is dropped from 10 meters. What is its velocity just before hitting the ground?

Solution Steps:

1Initial: PE = mgh = 2 × 9.81 × 10 = 196.2 J, KE = 0
2Final: PE = 0, KE = 196.2 J (conservation)
3Solve for v: ½mv² = 196.2
4v² = 2 × 196.2 / 2 = 196.2
5v = √196.2 = 14 m/s

Result:

Final velocity = 14 m/s (≈ 50 km/h)

Tips & Best Practices

✓KE = ½mv²: Doubling velocity quadruples kinetic energy, but doubling mass only doubles it
✓PE = mgh: Potential energy depends on your choice of reference point (usually ground level)
✓Conservation: In closed systems without friction, total mechanical energy (KE + PE) stays constant
✓Unit conversions: 1 kWh = 3.6 MJ, 1 Cal (food) = 4.184 kJ, 1 BTU = 1.055 kJ
✓Efficiency: Real systems always lose some energy to heat due to friction and other factors
✓Work = Force × Distance: Energy is transferred when forces act over distances
✓E = mc²: Mass and energy are equivalent; tiny mass = enormous energy due to c²

Frequently Asked Questions

One Joule is the energy needed to lift a small apple (about 100 grams) one meter high, or the kinetic energy of a tennis ball moving at 6 m/s. It's also the energy used by a 1-watt device in 1 second. A food Calorie equals 4,184 Joules—so eating an apple (~50 Cal) provides about 200,000 Joules of chemical energy.

Because KE = ½mv², and velocity is squared. If v doubles, v² quadruples. This has critical safety implications: a car at 60 mph has four times the kinetic energy of the same car at 30 mph, requiring four times the stopping distance (assuming same braking force). This is why high-speed crashes are so much more dangerous.

Yes! Total energy is always conserved—it just changes form. When a ball bounces and gradually stops, kinetic energy converts to: 1) thermal energy (the ball and floor warm up slightly), 2) sound energy (you hear the bounces), and 3) deformation energy. The energy isn't lost; it's just no longer in a useful mechanical form.

A typical US household uses about 900 kWh per month, which equals 3.24 billion Joules (3.24 GJ). For perspective: a refrigerator uses ~1-2 kWh/day, air conditioning 3-5 kWh/hour when running, and a single LED bulb about 0.01 kWh/hour. Electricity costs roughly $0.12-0.30 per kWh depending on location.

Energy is a quantity (measured in Joules), while power is a rate (Joules per second = Watts). A 100W light bulb uses energy at 100 J/s. Running for 1 hour, it uses 100W × 3600s = 360,000 J = 0.1 kWh. Think of power as how fast you use energy, and energy as the total amount used.

The energy equivalent of mass is enormous. One kilogram of mass, if fully converted to energy, would release 9 × 10¹⁶ Joules—equivalent to about 21 megatons of TNT, or roughly 1,500 Hiroshima bombs. Nuclear reactions convert only about 0.1% of mass to energy, but that's still tremendous. This is why nuclear energy is so powerful compared to chemical energy.

Sources & References

Halliday, Resnick & Walker - Fundamentals of Physics (2024)
MIT OpenCourseWare - Energy and Work (2024)
U.S. Energy Information Administration (2024)
NIST - SI Units for Energy (2024)

Last updated: 2026-01-22

Energy Calculator

Kinetic Energy (KE = 0.5mv²)

Gravitational Potential Energy (PE = mgh)

Elastic Potential Energy (PE = 0.5kx²)

Energy from Power (E = Pt)

Energy Formulas

What is Energy?

Energy Unit Definition

Kinetic Energy

Kinetic Energy Formula

Potential Energy

Gravitational Potential Energy

Work-Energy Theorem

Work-Energy Theorem

Conservation of Energy

Conservation of Mechanical Energy

Energy Units and Conversions

Mass-Energy Equivalence

Mass-Energy Equivalence

Worked Examples

Kinetic Energy of a Vehicle

Potential Energy at Height

Conservation of Energy - Falling Object

Tips & Best Practices

Related Calculators

Frequently Asked Questions

Sources & References