Momentum Calculator
Momentum is one of the most fundamental quantities in classical mechanics. Linear momentum (p) is defined as the product of an object's mass and its velocity: p = m * v. It is a vector quantity measured in kilogram-metres per second (kg m/s). The greater an object's mass or speed, the more momentum it carries and the more force or time is needed to change its motion. Closely related is the concept of impulse (J), which measures the change in momentum produced by a force acting over a time interval: J = F * t. The impulse-momentum theorem states that the net impulse on a body equals its change in momentum, making impulse the practical tool for analysing collisions, car crashes, and sports contacts. The law of conservation of momentum states that in a closed system free of external forces, the total momentum is constant. This calculator covers three scenarios: single-object momentum, impulse from force and time, and combined momentum for two objects to illustrate conservation. Enter your values below. All inputs accept decimal and comma-formatted numbers.
Momentum: -- kg m/s | Impulse: -- N s
Part 1: Linear Momentum (p = m × v)
Part 2: Impulse (J = F × t)
Part 3: Total Momentum (two objects)
How momentum is calculated
Linear momentum is the product of mass and velocity. Because velocity is a vector, momentum is also a vector pointing in the same direction as the velocity. Two objects moving in opposite directions have momenta with opposite signs.
p = m × v
where p = momentum (kg m/s), m = mass (kg), v = velocity (m/s)
Impulse-momentum theorem
J = F × t = Δp = m × Δv
where J = impulse (N s), F = net force (N), t = time (s)
Conservation of momentum
p_total = p1 + p2 = m1 × v1 + m2 × v2
Worked example
A 10 kg object moves at 5 m/s:
- p = 10 kg × 5 m/s = 50.00 kg m/s
A 20 N force acts for 3 s:
- J = 20 N × 3 s = 60.00 N s
Two objects: m1 = 5 kg at 4 m/s, m2 = 8 kg at 2 m/s:
- p1 = 5 × 4 = 20 kg m/s
- p2 = 8 × 2 = 16 kg m/s
- p_total = 20 + 16 = 36.00 kg m/s
Momentum calculator: frequently asked questions
What is linear momentum?
Linear momentum is the product of an object's mass and its velocity: p = m * v. It is a vector quantity, meaning it has both magnitude and direction. The SI unit of momentum is the kilogram-metre per second (kg m/s). A heavier or faster object carries more momentum than a lighter or slower one.
What is impulse and how does it relate to momentum?
Impulse (J) is the change in momentum produced when a force acts over a time interval: J = F * t = delta_p. The impulse-momentum theorem states that the net impulse on an object equals the change in its momentum. Units are the same: newton-seconds (N s) or equivalently kg m/s.
What is conservation of momentum?
In a closed system with no external forces, the total momentum before an event equals the total momentum after: p1_initial + p2_initial = p1_final + p2_final. This law applies to collisions (elastic and inelastic) and explosions. It follows directly from Newton's third law of motion.
What are the units of momentum?
The SI unit of momentum is kilogram-metre per second (kg m/s), which is equivalent to newton-second (N s). In CGS units momentum is measured in gram-centimetre per second (g cm/s). The equivalence N s = kg m/s arises because 1 N = 1 kg m/s².
How does mass affect momentum?
Momentum is directly proportional to mass. Doubling an object's mass doubles its momentum at the same velocity. This is why a heavy truck travelling at highway speed carries far more momentum than a bicycle at the same speed, making it much harder to stop. The same principle underlies the stopping distance differences between vehicles.
Official sources
- NIST SP 330 (2019) "The International System of Units (SI)": NIST SP 330 PDF.
- NIST SI Unit definitions: nist.gov SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.