Calculate momentum, mass, or velocity with correct units, and use 1D signs or 2D x/y components so direction is handled clearly.
Advanced options
How to use our Momentum Calculator
- Choose What do you want to calculate? (mode): Momentum for motion (
p = m*v) or Impulse for a push over time (J = F*delta t). - Pick Direction setup (1D or 2D): use 1D if you can describe direction with + or -, or 2D if you have x and y components.
- In Momentum mode, set Solve for (Momentum mode) to the value you want: Momentum (p), Mass (m), or Velocity (v).
- Enter Mass (selected unit) and select the correct Mass unit for the number you typed (kg, g, or lb).
- Enter the motion values for your direction setup: for 1D, use Velocity (selected unit, 1D signed) or Momentum (selected unit, 1D signed); for 2D, use Velocity x-component (selected unit) and Velocity y-component (selected unit) (and the calculator will compute p_x, p_y, and magnitude).
- Set Velocity unit and Momentum unit. If you want a specific look for big or tiny numbers, set Number display format to Auto, Plain, or Scientific.
- Open Advanced options if you want a different Output momentum unit (Momentum results) or you want Show SI breakdown (kg, m/s, N*s) to see the converted SI values.
- In Impulse mode, choose Solve for (Impulse mode) and enter any two of Average force (selected unit, signed), Contact time (selected unit), and Impulse / change in momentum (selected unit, signed). If you also enter Mass (selected unit) and Initial velocity (selected unit, 1D signed, for finding final velocity), you can get an estimated final velocity in 1D.
- Click Calculate, then sanity-check: (a) does the sign match your chosen positive direction, and (b) do the units make sense (for example, mph converts to a smaller number in m/s).
Definitions
Momentum (p): A measure of motion equal to mass times velocity. It is a vector, so direction matters. [1]
Mass (m): How much matter an object has. In this tool, it is the value in Mass (selected unit) with the matching Mass unit.
Velocity (v): Speed with direction. In 1D, direction is shown by a + or - sign. [2]
1D (signed) vs 2D (components): 1D uses one signed number. 2D uses x and y parts (components), like Velocity x-component (selected unit) and Velocity y-component (selected unit).
Impulse (J) / change in momentum (delta p): The change in momentum caused by a force acting over a time interval. In this tool, Impulse / change in momentum is treated as the same quantity. [1]
Average force (F): A single force value that represents the overall push during the contact time (not necessarily the peak force).
Unit equivalence (N*s and kg*m/s): In SI units, 1 newton-second equals 1 kilogram-meter-per-second, so the same momentum can be written either way. [3]
Common mistakes and quick fixes
Mistake: Forgetting that direction matters and entering a positive value when it should be negative in Velocity (selected unit, 1D signed) , Momentum (selected unit, 1D signed) , or Average force (selected unit, signed) .
Fix: Decide what counts as the positive direction first, then use a minus sign for anything pointing the opposite way and recalculate.
Mistake: Choosing Direction setup (1D or 2D) = 2D but expecting the 1D velocity or 1D momentum boxes to affect the answer.
Fix: In 2D, enter Velocity x-component (selected unit) and Velocity y-component (selected unit) (or Momentum x-component (selected unit) and Momentum y-component (selected unit) when relevant) because hidden 1D rows are ignored.
Mistake: Trying to solve Mass (m) with Velocity (selected unit, 1D signed) = 0 (or trying to solve Average force (F) with Contact time (selected unit) = 0).
Fix: Avoid divide-by-zero: use a nonzero velocity to compute mass from m = p/v , and use a positive contact time to compute force from F = J/delta t .
Mistake: Mixing units, like typing pounds but leaving Mass unit on kg, or typing mph but leaving Velocity unit on m/s.
Fix: Make the unit selectors match the numbers you typed, then recalculate. Turn on Show SI breakdown (kg, m/s, N*s) to double-check the converted SI values.
Mistake: Expecting Estimated change in velocity (delta v, 1D) or Estimated final velocity (v_final, 1D) when mass is missing or not greater than 0.
Fix: Enter a positive Mass (selected unit) , then enter or compute Impulse / change in momentum (selected unit, signed) . Add Initial velocity (selected unit, 1D signed, for finding final velocity) if you want v_final .
Limitations & Key Assumptions / Boundary Conditions
Scope: Momentum mode uses linear momentum (p = m*v). Impulse mode uses average force over a time interval (J = F*delta t). If force changes a lot during contact, a single average force may not match the real peak force or detailed force curve.
Direction is your choice: In 1D, negative inputs mean opposite your chosen positive direction. The calculator cannot know what you meant by "left" or "right" or which direction your class defines as positive.
Undefined cases (divide-by-zero): Solving Mass (m) from m = p/v requires velocity not equal to 0. Solving Average force (F) from F = J/delta t requires contact time greater than 0. Solving Contact time (delta t) from delta t = J/F requires force not equal to 0.
Not-unique cases: If momentum is 0 and velocity is 0, then p = m*v is true for many masses, so mass cannot be uniquely determined from those two zeros.
Positive mass requirement: To compute Velocity (v) from v = p/m, or to estimate delta v and v_final in Impulse mode, mass must be greater than 0.
2D reporting: In 2D, the tool outputs components and magnitudes (like |p|). It does not output an angle, compass direction, or a diagram.
Conversions and rounding: Unit conversions are exact or standard, but the displayed number is rounded. Auto/Scientific display may show scientific notation for very large or very small results; this changes the look, not the value.
Methodology
The calculator uses standard linear momentum and impulse relationships, keeping direction with a sign in 1D or with x/y components in 2D. Momentum is a vector (direction matters), so negative results are allowed and meaningful. [1]
Momentum (1D): p = m * v
Solve mass: m = p / v (requires v != 0)
Solve velocity: v = p / m (requires m > 0)
Momentum (2D): p_x = m * v_x; p_y = m * v_y
Magnitudes (2D): |v| = sqrt(v_x^2 + v_y^2); |p| = sqrt(p_x^2 + p_y^2)
Impulse: J = F_avg * delta t = delta p
Solve force: F_avg = J / delta t (requires delta t > 0)
Solve time: delta t = J / F_avg (requires F_avg != 0)
Impulse to velocity (1D): delta v = (delta p) / m; v_final = v_initial + delta v (requires m > 0)
Units: inputs are converted to SI internally (kg, m/s, s, N) before calculating, then converted back for display. The tool may show that 1 N*s equals 1 kg*m/s (same numeric value). [3]
Worked mini-example (Momentum, 1D): Let mass = 2 kg and velocity = -3 m/s (negative means opposite your chosen positive direction). Then momentum p = 2 * (-3) = -6 kg*m/s. [2]
Worked mini-example (2D components): Let mass = 2 kg, v_x = 3 m/s, v_y = 4 m/s. Then p_x = 6 kg*m/s, p_y = 8 kg*m/s, |v| = 5 m/s, and |p| = 10 kg*m/s.
Worked mini-example (Impulse): Let average force = 800 N and contact time = 0.12 s. Then impulse J = 800 * 0.12 = 96 N*s, which is also 96 kg*m/s. [1]
If an equation would require dividing by zero (like v = 0 when solving m, or delta t = 0 when solving F), the calculator marks those outputs as N/A and lists the exact issue in Notes or warnings.