Work Power Energy Formula Sheet: Every Equation in One Place

This work power energy formula sheet collects the equations of the chapter on one page, starting with the definition of work, $W = Fs\cos\theta$ . From that one line come kinetic energy, the work energy theorem, potential energy, conservation of mechanical energy and power, so the tables below follow that order.

It suits Class 11 work, energy and power, the AP Physics 1 energy unit, and the mechanics part of JEE Main and NEET. It is a revision summary written for this site, not an official exam sheet. Each row links to a page with worked examples. More course sheets are listed on the formula sheets hub.

Quick facts

Starting point
$W = Fs\cos\theta$
Energy unit
joule, 1 J = 1 N m
Power unit
watt, 1 W = 1 J/s
Other units
1 kWh = 3.6 × 10⁶ J, 1 hp ≈ 746 W, 1 eV = 1.602 × 10⁻¹⁹ J
Big idea
Net work changes kinetic energy
Courses
Class 11, AP Physics 1, JEE Main, NEET

Work formulas

Ways to calculate work
Relation	Use it to find	Unit	Full page
$W = Fs\cos\theta$	work done when the force stays fixed	J	Work
$W = \vec{F}\cdot\vec{s}$	the same, in dot product form	J	Work
$W = \int F\,dx$	work by a varying force, area under F against x	J	Work and energy
$W_f = -\mu_k N d$	energy removed by sliding friction	J	Work done by friction
$W_g = -mg\,\Delta h$	work by gravity when height changes by Δh	J	Potential energy

Work is positive when the force has a component along the motion, zero when the force is perpendicular (θ = 90°), and negative when it opposes the motion. Zero work also comes from a level floor's normal force and from the string tension that keeps a whirled stone on its circle.

Energy formulas: kinetic, potential and the theorem

Kinetic and stored energy
Relation	Use it to find	Unit	Full page
$KE = \frac{1}{2}mv^2$	energy of motion	J	Kinetic energy
$KE = \frac{p^2}{2m}$	kinetic energy from momentum	J	Momentum
$PE = mgh$	gravitational energy near the ground	J	Potential energy
$U = \frac{1}{2}kx^2$	elastic energy of a spring	J	Spring potential energy
$W_{net} = K_f - K_i$	speed after net work is done	J	Work energy theorem
$KE_i + PE_i = KE_f + PE_f$	speeds and heights with only conservative forces	J	Conservation of energy

Revision problem 1: a sledge on a hill

A sledge and rider, 40 kg in total, are released from a standstill on a snowy slope 4.5 m high. Ignoring friction, how fast is the sledge moving at the bottom? If friction does −900 J of work on the way down, what is the speed instead?

Without friction: $mgh = \frac{1}{2}mv^2$ , so $v = \sqrt{2gh} = \sqrt{2(9.8)(4.5)} = \sqrt{88.2} = 9.4\ \text{m/s}$ .

With friction: $(40)(9.8)(4.5) - 900 = \frac{1}{2}(40)v^2$ , so $1764 - 900 = 864 = 20v^2$ and $v = \sqrt{43.2} = 6.6\ \text{m/s}$ .

Answer: 9.4 m/s without friction, 6.6 m/s with it.

Power and efficiency

Rate of doing work
Relation	Use it to find	Unit	Full page
$P = \frac{W}{t}$	average power	W	Work and energy
$P = Fv\cos\theta$	instantaneous power of a force on a moving body	W	Force
$\eta = \frac{\text{useful output}}{\text{input}} \times 100\%$	efficiency of a machine	no unit	Energy
$E = Pt$	energy used by an appliance	J or kWh	Energy

Revision problem 2: a water pump

An electric pump lifts 500 kg of water through a height of 10 m in 50 s. Find its useful power output. If the pump is 70% efficient, what is its input power?

Useful work: $W = mgh = (500)(9.8)(10) = 49\,000\ \text{J}$ .

Useful power: $P = \frac{49\,000}{50} = 980\ \text{W}$ . Input power: $\frac{980}{0.70} = 1400\ \text{W} = 1.4\ \text{kW}$ .

Answer: 980 W useful output, 1.4 kW drawn.

Collisions and circular motion in a vertical plane

Results that JEE and NEET papers lean on
Relation	Use it to find	Unit	Full page
$e = \frac{\text{separation speed}}{\text{approach speed}}$	bounciness of an impact	no unit	Coefficient of restitution
$p_{1i} + p_{2i} = p_{1f} + p_{2f}$	total momentum before equals total after, in any collision	kg m/s	Momentum conservation
$v_A = u_B,\ v_B = u_A$	equal masses, elastic and head on: the velocities swap	m/s	Kinetic energy
$v = \frac{p_{total}}{m_1 + m_2}$	common velocity when the bodies stick together	m/s	Momentum
$v_{top} \ge \sqrt{gr}$	minimum speed needed at the highest point of a string loop	m/s	Circular motion
$v_{bottom} \ge \sqrt{5gr}$	minimum speed at the lowest point to go all the way round	m/s	Circular motion

Kinetic energy is conserved only when e = 1. Sticking together is the case that throws away the most kinetic energy momentum conservation permits.

How to revise from this work power energy formula sheet

Learn the chain, not a list. Work leads to the theorem, the theorem leads to potential energy, and the two together give conservation.
Check which forces do work. Perpendicular forces do none; friction always takes energy out of a sliding body.
Convert units first. km/h becomes m/s after division by 3.6, grams to kilograms, kWh to joules by multiplying by 3.6 × 10⁶.
Use energy for speeds, forces for times. Energy methods give no time information.

For the chapter in other courses, see the Class 11 chapter wise formulas, the AP Physics 1 formula sheet and the NEET physics formula sheet.

Frequently asked questions

What are the main formulas in work, power and energy?

W = Fs cos θ for work, KE = ½mv² for kinetic energy, PE = mgh and ½kx² for stored energy, W_net = ΔKE for the work energy theorem, and P = W/t = Fv for power.

How are work and power different?

Work is the energy transferred by a force, in joules. Power is how fast that transfer happens, in watts, so P = W/t.

Does work have a direction?

No. Work is a scalar: force and displacement are vectors, but their dot product is just a signed number.

How many joules are in one kilowatt hour?

Multiply 1000 W by one hour, which is 3600 s, and you get 3.6 × 10⁶ J. Household meters count energy in kWh.

Can I use this page as my exam sheet?

No. Treat it as revision notes written for practice. Exam boards supply their own sheets wherever one is permitted.