Physics Calculator: How to Solve Force, Velocity, Acceleration, and Energy Problems Step by Step

Physics is all around you — from the force needed to push a car up a hill to the velocity of a baseball pitch or the energy consumed by a household appliance. Whether you are a student studying for an exam, a hobbyist working on a project, or a professional engineer, having the right formulas and a reliable calculator makes solving physics problems straightforward.

Try our free Physics Calculator to solve force, velocity, acceleration, work, and energy problems instantly.

Essential Physics Formulas Reference

Concept	Formula	Variables	Example
Force	F = m × a	m = mass (kg), a = acceleration (m/s²)	10 kg × 5 m/s² = 50 N
Velocity	v = d / t	d = distance (m), t = time (s)	100 m / 10 s = 10 m/s
Acceleration	a = Δv / Δt	Δv = change in velocity (m/s), Δt = time (s)	(20-0) m/s / 4 s = 5 m/s²
Kinetic Energy	KE = ½mv²	m = mass (kg), v = velocity (m/s)	½ × 2 kg × (10 m/s)² = 100 J
Potential Energy	PE = m × g × h	g = gravity (9.8 m/s²), h = height (m)	5 kg × 9.8 × 2 m = 98 J
Work	W = F × d	F = force (N), d = distance (m)	50 N × 10 m = 500 J
Power	P = W / t	W = work (J), t = time (s)	500 J / 5 s = 100 W
Momentum	p = m × v	m = mass (kg), v = velocity (m/s)	2 kg × 10 m/s = 20 kg·m/s

Step-by-Step Problem Solving

Problem 1: Calculating Force

Scenario: You push a 20 kg shopping cart with an acceleration of 1.5 m/s². How much force are you applying?

1. Identify the formula: F = m × a
2. Plug in values: F = 20 kg × 1.5 m/s²
3. Calculate: F = 30 N (newtons)

Problem 2: Finding Velocity

Scenario: A train travels 500 meters in 25 seconds. What is its velocity?

1. Identify the formula: v = d / t
2. Plug in values: v = 500 m / 25 s
3. Calculate: v = 20 m/s (about 72 km/h or 45 mph)

Problem 3: Kinetic Energy of a Baseball

Scenario: A baseball (0.145 kg) is thrown at 40 m/s (about 90 mph). How much kinetic energy does it have?

1. Identify the formula: KE = ½ × m × v²
2. Plug in values: KE = 0.5 × 0.145 × (40)²
3. Calculate: KE = 0.5 × 0.145 × 1600 = 116 joules

Real-World Physics Applications

• Car safety: Understanding force and deceleration helps design crumple zones and airbags. A 70 kg passenger in a car stopping from 60 km/h (16.7 m/s) in 0.3 seconds experiences about 3,900 N of force — that is why seatbelts save lives.
• Sports: Tennis players use F = m × a to calculate how hard to hit the ball. A 0.058 kg tennis ball accelerated at 500 m/s² requires 29 N of force.
• Renovation: Calculating the work needed to lift building materials. Lifting a 50 kg bag of cement 3 meters requires 50 × 9.8 × 3 = 1,470 J of work.
• Exercise: Power output during weightlifting. Lifting 100 kg a height of 1 meter in 2 seconds requires 100 × 9.8 × 1 ÷ 2 = 490 watts.

Unit Conversion Tips for Physics

Convert	Formula
km/h to m/s	Divide by 3.6 (e.g., 72 km/h ÷ 3.6 = 20 m/s)
g to kg	Divide by 1000 (e.g., 500 g ÷ 1000 = 0.5 kg)
cm to m	Divide by 100 (e.g., 150 cm ÷ 100 = 1.5 m)
mph to m/s	Multiply by 0.447 (e.g., 60 mph × 0.447 = 26.8 m/s)

For any physics calculation, use our Physics Calculator — it handles force, velocity, acceleration, kinetic energy, potential energy, work, power, and momentum with any unit system.