Physics calculator
Momentum Calculator
Calculate an object's linear momentum from its mass and velocity.
Momentum
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How the mass and velocity fields work
Mass and velocity each get their own unit dropdown, and the two are independent of one another. Mass can be entered in kilograms, grams, or pounds; velocity in meters per second, kilometers per hour, or miles per hour. Behind the scenes every mass is converted to kilograms (grams divided by 1,000, pounds multiplied by 0.45359237) and every velocity to meters per second (kilometers per hour divided by 3.6, miles per hour multiplied by 0.44704), so the result is always reported in kg·m/s no matter which units you picked.
The mass field rejects negative numbers, since a negative mass has no physical meaning, but the velocity field does not — a negative velocity is simply motion in the negative direction. That is why the result panel includes a direction line reading "Positive direction," "Negative direction," or "At rest," rather than treating a negative momentum as an error.
The momentum formula
Multiply mass by velocity and the units multiply along with the numbers: kilograms times meters per second gives kilograms times meters per second, written kg·m/s. A 10 kg mass moving at 3 m/s carries 10 × 3 = 30 kg·m/s of momentum.
Unit conversion happens before the multiplication, not after. For a 150 lb object moving at 10 mph: 150 lb × 0.45359237 = 68.0388555 kg, and 10 mph × 0.44704 = 4.4704 m/s, so momentum is 68.0388555 × 4.4704 ≈ 304.1609 kg·m/s. A 0.008 kg (8 g) bullet at 400 m/s carries only 0.008 × 400 = 3.2 kg·m/s, far less than the 150 lb example, because momentum scales with mass just as directly as it scales with speed.
Momentum is a vector; this tool reports a signed magnitude
Physicists treat momentum as a vector with a direction, but this calculator works along a single line, so the sign of your velocity input is the only direction information it carries. It cannot add two momentum vectors that point at an angle to each other — for a car moving north and one moving east, you would need to resolve each into components first.
The tool also does not perform collision calculations. To check conservation of momentum in a two-object collision (m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′), run each object's momentum through the calculator separately, keep track of the signs by hand, and add the results yourself.
Momentum in familiar situations
Plugging in everyday numbers shows how much mass and speed each contribute:
- A 1,500 kg car at 15 m/s (54 km/h) carries 1,500 × 15 = 22,500 kg·m/s
- A regulation 0.145 kg baseball pitched at 40 m/s carries 0.145 × 40 = 5.8 kg·m/s
- An 8 g bullet at 400 m/s carries 0.008 × 400 = 3.2 kg·m/s
- A 60 kg skater pushing off at 2 m/s carries 60 × 2 = 120 kg·m/s
- A 50,000,000 kg cargo ship easing into a berth at 0.5 m/s carries 25,000,000 kg·m/s, which is why tugboats are needed even at walking pace
Frequently asked questions
Can momentum come out negative?
Yes. Mass can't be negative in this calculator, but velocity can be, and a negative velocity produces a negative momentum. The result panel labels it "Negative direction" rather than treating it as an invalid answer.
Do the mass unit and velocity unit need to match?
No. Choose kg, g, or lb for mass and m/s, km/h, or mph for velocity independently — each is converted to SI (kilograms and meters per second) before the multiplication, so any combination works.
Why is the answer always in kg·m/s, even if I entered pounds and mph?
The calculator converts every input to kilograms and meters per second internally and only converts back for display in the input fields, not the result. The output is always kg·m/s regardless of which units you chose for mass or velocity.
How is momentum different from kinetic energy?
Momentum is p = mv and scales linearly with speed; kinetic energy is KE = ½mv² and scales with the square of speed. Doubling a 10 kg object's velocity from 3 m/s to 6 m/s doubles its momentum from 30 to 60 kg·m/s, but quadruples its kinetic energy.
Can I use this to check momentum conservation in a collision?
You can compute the momentum of each object separately — before and after — but the tool doesn't sum them for you. Note the sign of each velocity carefully, since a collision problem usually has objects moving in opposite directions.
Why does a negative mass produce a blank result?
The mass field has a minimum of zero because negative mass isn't physical, so the calculator withholds a result rather than compute a meaningless number from an invalid input.