Momentum & Impulse Calculator (p = mv)

Calculate linear momentum, mass, or velocity using p = mv. Analyze impulse (N·s), kinetic energy (J), and collision impact physics with real-world transport benchmarks.

Target Parameter

Live calculation
Quick Sample Presets
kg
m/s
Calculated Momentum
20,100 kg·m/svia p = m × v
Equivalent Impulse20,100 N·s

Kinetic Energy

134.7 kJ

Velocity (mph)

30.0 mph

Velocity (km/h)

48.2 km/h

Mass (kg)

1500.0 kg

Collision Stopping Forces (F = Δp / Δt)

0.2s Quick Hard Impact (Airbag / Barrier)

100,500 N (22593 lbf)

3.0s Controlled Emergency Brake

6,700 N (1506 lbf)

A 1500.0 kg body traveling at 13.4 m/s has a momentum of 20,100 kg·m/s.

To bring this body to a complete halt requires an impulse of 20,100 N·s.

The Fundamental Physics of Linear Momentum ($p = mv$)

In Newtonian classical mechanics, linear momentum ($p$) represents the quantitative measure of an object's translational inertia in motion. Defined as the mathematical product of mass and velocity ($p = m \times v$), momentum is a directional vector quantity governed by universal conservation laws.

Linear Momentum & Impulse Core Equations
1. Solve Momentum (p)
p = m × v

kg·m/s = kg × (m/s)

2. Solve Mass (m)
m =
p (momentum)v (velocity)

kg = (kg·m/s) ÷ (m/s)

3. Solve Velocity (v)
v =
p (momentum)m (mass)

m/s = (kg·m/s) ÷ kg

Impulse-Momentum Theorem & Kinetic Energy Relation
Impulse J = F × Δt = Δp|1 kg·m/s = 1 N·s|KE = p² / (2m)
Step-by-Step Calculation Breakdown
Example 1: 1,500 kg Vehicle at 13.4 m/s (30 mph City Speed)
1. Parameters: Mass m = 1,500.00 kg, Velocity v = 13.40 m/s
2. Calculate momentum: p = 1,500.00 × 13.40 = 20,100.00 kg·m/s (20,100.00 N·s)
3. Associated kinetic energy: KE = ½ × 1,500 × 13.4² = 134,670.00 Joules (134.67 kJ)
Example 2: 36,000 kg Semi-Trailer at 26.8 m/s (60 mph Highway Speed)
1. Parameters: Semi mass m = 36,000.00 kg, Velocity v = 26.80 m/s
2. Calculate momentum: p = 36,000.00 × 26.80 = 964,800.00 kg·m/s
3. Ratio analysis: The semi carries 48× the momentum of the sedan, explaining why commercial trucks require massive stopping distances.

Comparative Momentum Reference Benchmarks

Moving Object / SystemMass (kg)Velocity (m/s)Momentum (kg·m/s)
Falling apple (100g at 1.0 m/s)0.1 kg1.0 m/s0.1
Walking adult (70 kg at 1.4 m/s / 3 mph)70 kg1.4 m/s98
Sprinter sprinting (80 kg at 10.0 m/s / 22 mph)80 kg10.0 m/s800
Fired handgun bullet (8g at 350 m/s)0.008 kg350.0 m/s2.8
Compact sedan at city speed (1,200 kg at 13.4 m/s / 30 mph)1,200 kg13.4 m/s16,080
Commercial semi-truck at highway speed (36,000 kg at 26.8 m/s / 60 mph)36,000 kg26.8 m/s964,800
Freight train consist (5,000,000 kg at 15.0 m/s / 33 mph)5,000,000 kg15.0 m/s75,000,000

Frequently Asked Questions

What is linear momentum and why is it conserved?
Linear momentum (p) is the vector product of an object's mass (m) and its velocity (v): p = m × v. Measured in kg·m/s (or N·s), momentum is universally conserved in closed physical systems because internal action-reaction force pairs cancel out (Newton's Third Law).
How does impulse relate to momentum and vehicular collision safety?
Impulse (J) is defined as the integral of force over time: J = F × Δt = Δp (change in momentum). Airbags and crumple zones save lives by dramatically extending the duration (Δt) of a collision. For a fixed momentum change, increasing Δt decreases the peak impact force (F = Δp / Δt) experienced by vehicle occupants.
What is the difference between elastic and inelastic collisions?
In both elastic and inelastic collisions, total linear momentum is 100% conserved. However, in elastic collisions, total mechanical kinetic energy is also preserved, whereas in inelastic collisions, kinetic energy is partially converted into internal thermal heat, structural plastic deformation, and sound.
How is momentum different from kinetic energy?
Momentum (p = mv) is a vector that scales linearly with velocity. Kinetic energy (KE = ½mv²) is a scalar that scales with velocity squared. A bullet and a heavy walking person can have similar linear momentum, but the bullet carries vastly higher kinetic energy due to its high velocity.

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