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Impulse Calculator
Calculate impulse, force, or time using J = F x t. Understand the impulse-momentum theorem with step-by-step solutions.
Formula:
Results
Impulse50 N·s
Impulse (SI)50 N·s
Force (SI)10 N
Time (SI)5 s
Momentum Change50 kg·m/s
Peak Force (est.)20 N
Impulse Formula: J = F x t
Enter values to calculate impulse, force, or time
Applied force
Duration of force
Impulse
50 N·s
Calculated value
Impulse
50 N·s
50 kg·m/s
Average Force
10 N
Peak: ~20 N
Duration
5000 ms
5 s
Impulse Calculation (J = F × Δt)
1
Identify the formula
J = F × Δt
Impulse equals force times time
2
Convert force to SI
F = 10 N = 10 N
3
Convert time to SI
Δt = 5 s = 5 s
4
Calculate impulse
J = 10 × 5
J = 50 N·s
Final Answer: 50 N·s
Force-Time Analysis
Average vs Peak Force
Average Force
10 N
F_avg = J / \u0394t
Estimated Peak Force
20 N
Assumes triangular profile (~2x average)
Safety Insight
Why airbags work: For the same momentum change (impulse), increasing impact time reduces force. If your impulse of 50 N\u00B7s occurred over 10x longer time, force would be only 1 N instead of 10 N.
Impulse Unit Conversions
Newton-seconds
50 N·s
Kilogram-meters/second
50 kg·m/s
Pound-force-seconds
11.2405 lbf·s
Quick Answer: What is Impulse?
Impulse (J) equals force times time: J = F × Δt. It also equals the change in momentum: J = Δp = mΔv. For example, a 10 N force applied for 5 seconds produces an impulse of 50 N·s (or 50 kg·m/s). Impulse is why airbags work—they increase impact time to reduce force.
Key Facts
- Impulse formula: J = F × Δt (Force times time interval)
- Impulse equals momentum change: J = Δp = mΔv
- SI units: Newton-seconds (N·s) = kilogram-meters per second (kg·m/s)
- Impulse is a vector quantity with the same direction as force
- Area under a force-time graph equals impulse
- Airbags and crumple zones increase time to reduce peak force
- For constant force: J = FΔt; for varying force: J = ∫F dt
Frequently Asked Questions
Impulse is the product of force and the time interval over which it acts: J = F × Δt. It represents the total effect of a force over time and equals the change in momentum of an object. The SI unit is newton-seconds (N·s), which is equivalent to kg·m/s.
Impulse equals the change in momentum: J = Δp = p_final - p_initial = m(v_final - v_initial). This is the impulse-momentum theorem. When a force acts on an object, it changes the object's momentum by an amount equal to the impulse delivered.
Airbags increase the time over which the collision occurs. Since impulse J = FΔt must equal the momentum change (which is fixed by the crash speed), increasing Δt means decreasing F. A crash that takes 0.1 seconds with an airbag versus 0.01 seconds without reduces the force by a factor of 10.
Average force is the constant force that would produce the same impulse: F_avg = J/Δt. Peak force is the maximum force during an impact, which can be 2-3 times the average. Real collisions have varying force profiles, with force building up and then decreasing.
Impulse equals the area under the force-time graph. For a constant force, it's simply F × Δt (a rectangle). For varying forces, calculate the area using geometry (triangles, trapezoids) or integration. This is why J = ∫F dt for non-constant forces.
Impulse is measured in Newton-seconds (N·s) in SI units. Since 1 N = 1 kg·m/s², we have 1 N·s = 1 kg·m/s. This equivalence makes sense because impulse equals change in momentum, which has units of kg·m/s.
In sports, impulse explains follow-through: keeping a bat, racket, or foot in contact with the ball longer increases impulse, thus increasing momentum transfer. A golf club in contact with the ball for 0.001 seconds delivers more impulse than a 0.0005-second contact at the same average force.
Yes, impulse is a vector quantity. If force and displacement are in opposite directions, the impulse is negative relative to your chosen positive direction. For example, a braking force produces negative impulse, reducing the object's momentum.
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Results
Impulse50 N·s
Impulse (SI)50 N·s
Force (SI)10 N
Time (SI)5 s
Momentum Change50 kg·m/s
Peak Force (est.)20 N