All calculatorsMomentum Calculator
Calculate momentum (p = m·v) and impulse (J = F·Δt = Δp) with unit conversion, 1D sign or 2D vector, and optional step-by-step.
Background
Momentum tells you how hard something is moving (mass × velocity). Impulse is the “push over time” that changes momentum. Note: 1 N·s = 1 kg·m/s.
How to use this calculator
- Pick Momentum, Impulse, or Collision.
- Fill the required fields (signs matter for direction).
- Use units you like (we convert behind the scenes).
- Click Calculate to get the answer + optional steps.
How this calculator works
- Momentum: converts inputs to SI, then uses p = m·v.
- Impulse: uses J = F·Δt and reports Δp (same value).
- Collision (1D): conserves momentum; elastic also conserves kinetic energy.
- For 2D momentum, it computes component-wise momentum and magnitudes.
Formula & Equation Used
Momentum: p = m·v
Impulse: J = F·Δt
Change in momentum: Δp = J
2D magnitude: |p| = √(pₓ² + pᵧ²)
Perfectly inelastic: vf = (m₁v₁ + m₂v₂)/(m₁ + m₂)
Example Problem & Step-by-Step Solution
Example 1 — Baseball thrown at 40 m/s
- Mass: m = 0.145 kg
- Velocity: v = 40 m/s
- Momentum: p = m·v = 0.145·40 = 5.8 kg·m/s
Example 2 — Car traveling at 72 km/h
- Mass: m = 1500 kg
- Convert speed: 72 km/h = 20 m/s
- Momentum: p = 1500·20 = 30,000 kg·m/s
Example 3 — Impulse from a bat hit
- Average force: F = 800 N
- Contact time: Δt = 0.12 s
- Impulse: J = F·Δt = 800·0.12 = 96 N·s
- So Δp = 96 kg·m/s (same quantity).
Frequently Asked Questions
Q: Is N·s the same as kg·m/s?
Yes. They are equivalent units of momentum/impulse.
Q: Why is my momentum negative?
In 1D, a negative sign just means the object is moving in the opposite direction you chose as positive.
Q: What if I’m using km/h or mph?
No problem—we convert everything to m/s internally.
