Momentum Calculator
Calculate momentum calculator calculate linear momentum p from mass m and velocity v (p = m * v). Accurate physics formulas and unit conversions for engineers, students & technicians.
Calculate Linear Momentum (p = m · v)
Enter your physical parameters below to compute verified momentum metrics.
Calculation Results
Calculated using verified physical methodology: Linear Momentum: p = m \cdot v
Kinetic Energy Relation: E_k = \p^2 / 2m
Quick Summary
The Momentum Calculator computes linear momentum ($p = m \cdot v$) by multiplying mass by velocity in SI ($\text{kg}\cdot\text{m/s}$ or $\text{N}\cdot\text{s}$) and Imperial units ($\text{lb}\cdot\text{ft/s}$).
Formula Explanation
Linear Momentum: p = m \cdot v
Kinetic Energy Relation: E_k = \p^2 / 2m
How It Works
The Momentum Calculator multiplies object mass ($m$ in kg) by velocity ($v$ in m/s). It outputs linear momentum in $\text{kg}\cdot\text{m/s}$, Newton-seconds ($\text{N}\cdot\text{s}$), Imperial $\text{lb}\cdot\text{ft/s}$, and calculates associated kinetic energy ($E_k = \p^2 / 2m$).
Step-by-Step Worked Example
Practical Problem: Calculate the momentum of a 1,200 kg passenger car traveling at $20.0\text{ m/s}$ (72 km/h).
- Step 1: Identify Input Values: Mass $m = 1,200\text{ kg}$, Velocity $v = 20.0\text{ m/s}$.
- Step 2: Apply the Momentum Formula: $p = m \cdot v$.
- Step 3: Execute Numeric Multiplication: $p = 1,200\text{ kg} \times 20.0\text{ m/s} = 24,000.00\text{ kg}\cdot\text{m/s}$.
- Step 4: Convert to Newton-Seconds & Imperial Units: $p = 24,000.00\text{ N}\cdot\text{s}$. Imperial: $24,000 \times 7.23301 = 173,592.24\text{ lb}\cdot\text{ft/s}$.
- Step 5: Calculate Associated Kinetic Energy: $E_k = \(24,000)^2 / 2 \times 1200 = \576,000,000 / 2,400 = 240,000.00\text{ Joules} = 240.00\text{ kJ}$.
Real-World Calculation Examples
Scenario 1: Highway Passenger Automobile
Parameters: $m = 1,200\text{ kg}$, $v = 20.0\text{ m/s}$ (72 km/h)
Result: $p = 24,000.00\text{ kg}\cdot\text{m/s}$ (24,000 N·s). Car linear momentum.
Scenario 2: Heavy Freight Train Transit
Parameters: $m = 500,000\text{ kg}$ (500 tonnes), $v = 15.0\text{ m/s}$ (54 km/h)
Result: $p = 7,500,000.00\text{ kg}\cdot\text{m/s}$ (7.50 MN·s). Massive train momentum.
Scenario 3: High-Velocity Rifle Bullet
Parameters: $m = 0.010\text{ kg}$ (10 g), $v = 800.0\text{ m/s}$
Result: $p = 8.00\text{ kg}\cdot\text{m/s}$ (8.00 N·s). High-speed bullet momentum.
Scenario 4: Professional Baseball Pitch
Parameters: $m = 0.145\text{ kg}$ (145 g), $v = 40.0\text{ m/s}$ (144 km/h)
Result: $p = 5.80\text{ kg}\cdot\text{m/s}$ (5.80 N·s). Baseball pitch momentum.
Key Benefits of Using This Calculator
Conservation of Momentum Support
Essential tool for evaluating elastic and inelastic collision dynamics.
Kinetic Energy Cross-Calculation
Automatically calculates kinetic energy ($E_k = \p^2 / 2m$) in Joules and kJ.
Multi-Unit Readouts
Provides momentum in $\text{kg}\cdot\text{m/s}$, $\text{N}\cdot\text{s}$, and Imperial $\text{lb}\cdot\text{ft/s}$.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is linear momentum?
Linear momentum (p) is a vector quantity measuring an object's mass in motion (p = m * v).
What is the formula for momentum?
p = m * v, where m is mass in kg and v is velocity in m/s.
What is the SI unit of momentum?
The SI unit of momentum is kilogram meter per second (kg·m/s), equivalent to Newton-seconds (N·s).
What is the Law of Conservation of Momentum?
In an isolated system with no external forces, total vector momentum before a collision equals total vector momentum after (Sigma p_initial = Sigma p_final).
How relates momentum to force?
Newton's Second Law states force is the time rate of change of momentum: F = dp / dt = d(m * v) / dt.
What is elastic vs inelastic collision?
In elastic collisions, both kinetic energy and momentum are conserved; in inelastic collisions, momentum is conserved but kinetic energy is lost as heat/deformation.
How converts kg·m/s to lb·ft/s?
Multiply kg·m/s by 7.23301 to get Imperial lb·ft/s (e.g. 24,000 kg·m/s = 173,592 lb·ft/s).
What is photon momentum?
Even though photons have zero rest mass, quantum mechanics gives photons momentum p = h / lambda = E / c.
What is relativistic momentum?
At near light speed c, relativistic momentum is p = (m * v) / sqrt(1 - v²/c²).
Is momentum a scalar or vector quantity?
Momentum is a vector quantity possessing both magnitude and direction matching velocity vector direction.