Newton’s second law ties together three things: how hard you push, how much there is to move, and how quickly it speeds up. This calculator solves F = ma for whichever of the three you are missing, with any mix of metric and US units. It suits physics homework, rough engineering checks, and questions like “what force does it take to get this cart moving at that rate?”
How to use the force calculator
- Under Solve for, choose Force, Mass or Acceleration.
- Enter the two known values. Force can be in N, kN, lbf, kgf, dyn or ozf; mass in kg, g, mg, metric tons, lb, oz, US tons or stone; acceleration in m/s², ft/s², g, km/h/s or mph/s.
- Use Show the result in to pick the unit of the answer. The result lists the same value in several other units, plus the acceleration expressed in g, and the steps show the formula, every unit conversion and the substitution.
F = ma and its rearrangements
Here F is the net force — the vector sum of every force acting on the object — not just the one you happen to be applying. Mass must be greater than zero. Force and acceleration may be negative: pick one direction along the line as positive, and a negative value points the other way. Because mass is positive, F and a always share a sign; when solving for mass, values with opposite signs are rejected, and so is an acceleration of zero (zero net force fits any mass).
Worked example
A 10 kg box is pushed so that it accelerates at 5 m/s².
F = 10 kg × 5 m/s² = 50 N
That is 0.05 kN, 11.24 lbf, 5.099 kgf or 5,000,000 dyn, and the acceleration is 0.51 g.
Summing forces first. A 2 kg model rocket has 50 N of thrust upward, and gravity pulls it down with 2 × 9.80665 = 19.61 N. Taking up as positive, the net force is 50 − 19.61 = 30.39 N, so a = 30.39 ÷ 2 = 15.19 m/s² (about 1.55 g). Using the 50 N thrust alone would overstate the acceleration by about 65%.
Force units and the newton
The SI unit of force, the newton, is defined in the BIPM’s SI Brochure as 1 kg·m/s². The others in the calculator are fixed multiples of it:
| Unit | Value in newtons | Where you meet it |
|---|---|---|
| dyne (dyn) | 0.00001 N exactly | CGS physics: 1 g·cm/s² |
| ounce-force (ozf) | 0.27801 N | small US spring scales |
| pound-force (lbf) | 4.4482216152605 N exactly | US engineering, thrust ratings |
| kilogram-force (kgf) | 9.80665 N exactly | older metric gauges, scales |
| kilonewton (kN) | 1,000 N | structures, vehicle loads |
The kilogram-force and pound-force are “weight” units: one kgf is the weight of 1 kg under standard gravity, and one lbf is the weight of 1 lb. For other conversions, the force converter covers every unit.
Common mistakes
- Using a weight as the mass. A bathroom scale reading of 70 kg is a mass, but 686 N is a weight. Putting the newton figure in the mass field makes everything about 9.8 times too large. The weight calculator converts between the two.
- Treating lb × ft/s² as lbf. In US units the formula needs the 32.174 conversion factor (or a mass in slugs). Choosing the units from the menus avoids it altogether.
- Forgetting other forces. Friction, drag, gravity on a slope and tension all enter the net force. Add them with signs before dividing by the mass; the friction calculator helps with the sliding part.
- Expecting force to keep things moving. Zero net force means zero acceleration, not zero speed. A puck gliding on ice at constant velocity has no net force on it.
The same law in its time form, FΔt = mΔv, is covered by the impulse-momentum calculator, and the acceleration calculator works from velocities and times instead of forces.
Frequently asked questions
What is Newton's second law?
The net force on an object equals its mass times its acceleration, F = ma. A 10 kg mass accelerating at 5 m/s² needs a net force of 50 N. The acceleration always points the same way as the net force.
What is one newton?
The force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg·m/s². It is about the weight of a small apple, and equals roughly 0.2248 pound-force.
How do I find mass from force and acceleration?
Divide: m = F ÷ a. A net force of 100 lbf producing 2 m/s² means a mass of 444.82 N ÷ 2 = 222.4 kg, or about 490 lb. Force and acceleration must have the same sign, and the acceleration cannot be zero.
Why do I get the wrong answer when I use pounds?
The pound is both a mass (lb) and a force (lbf). One lbf accelerates a 1 lb mass at 32.174 ft/s², not 1 ft/s², so 150 lb × 2 ft/s² is 9.32 lbf rather than 300. Pick each unit from its own menu and the calculator handles the conversion.