Force Calculator (F = ma)

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Choose a Calculation Solve for Force (F = m a) Solve for Mass (m = F / a) Solve for Acceleration (a = F / m)

F =

dyne (dyn) kilogram-force (kgf) newton (N) kilonewton (kN) kip (kip) pound-force (lbf) ounce-force (ozf) poundal (pdl)

m =

kilogram (kg) gram (g) pound avdp (lb) ounce avdp (oz)

a =

inch per second squared (in/s2) foot per second squared (ft/s2) centimeter per second squared (cm/s2) meter per second squared (m/s2) mile per second squared (mi/s2) mile per hour per second (mi/(h s)) kilometer per second squared (km/s2) kilometer per hour per second (km/(h s))

Significant Figures auto 3 4 5 6 7 8 9

Results

Force F

20

in selected force unit

Equation	F = m a (Newton's second law)

What is the Force Calculator?

This calculator applies Newton's second law of motion, \(F = m \cdot a\), the relationship that connects the net force acting on an object to its mass and the acceleration that force produces. Because the equation has three variables, you can solve for any one of them when the other two are known. The tool handles force, mass, and acceleration, and lets you choose units independently on each variable.

How to use it

First pick what you want to solve for using the "Choose a Calculation" dropdown. Enter the two known quantities, select their units, and the calculator returns the unknown in the unit you select for that variable. The "Significant Figures" option lets you round the answer to a fixed number of figures, or leave it on "auto" for full precision.

The formula explained

Internally every input is converted to SI base units (newtons for force, kilograms for mass, meters per second squared for acceleration) using exact scale factors. The unknown is computed in SI — \(F = m \cdot a\), \(m = \frac{F}{a}\), or \(a = \frac{F}{m}\) — and then converted back into the unit you chose. Because the conversions are symmetric, mixing non-SI input and output units always yields the same physically correct answer.

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Cover the unknown variable in the triangle to find \(F = m \cdot a\), \(m = \frac{F}{a}\), or \(a = \frac{F}{m}\).

Newton's second law: a net force F on mass m produces acceleration a in the same direction.

Worked example

Solve for force with \(m = 1500\ \text{lb}\) and \(a = 10\ \text{ft/s}^2\), output in pound-force. Convert: $$m = 1500 \times 0.45359237 = 680.39\ \text{kg}$$ $$a = 10 \times 0.3048 = 3.048\ \text{m/s}^2$$ Then $$F = 680.39 \times 3.048 = 2073.82\ \text{N}$$ Converting to pound-force: \(2073.82 / 4.4482216 \approx 466.2\ \text{lbf}\).

FAQ

Can force or acceleration be negative? Yes. A negative sign simply indicates direction, such as deceleration. Mass, however, must be a positive real number.

Why do I get an error? Solving for mass requires acceleration to be non-zero, and solving for acceleration requires mass to be non-zero, otherwise the formula divides by zero.

What is a newton? One newton is the force needed to accelerate a one-kilogram mass at one meter per second squared (\(1\ \text{N} = 1\ \text{kg}\cdot\text{m/s}^2\)).