How to Calculate Force (F = ma): Newton’s Second Law

Calculate force with F = ma. Net force vs weight, rearrangements, unit traps, worked examples, and a free force calculator.

What Force Asks

Newton’s second law says net force equals mass times acceleration. The same push that barely moves a heavy crate can send a light cart flying — mass sets how much acceleration you get for a given force.

The core formula is F = ma. Mass m in kilograms times acceleration a in m/s² gives force in newtons (N). One newton is the force that accelerates 1 kg at 1 m/s²: 1 N = 1 kg·m/s².

If you already have m and a (or F and one unknown), open the free force calculator first, then return here for net force, weight, and links to related tools.

The Formulas

  • F = ma — net force from mass and acceleration.
  • a = F / m — rearrange for acceleration.
  • m = F / a — rearrange for mass.
  • Weight near Earth: W = mg (a special case of F = ma with a = g).

    • F in F = ma is the net force — the vector sum of all forces after you cancel or combine them on a free-body diagram. A single push is not always the net force.

    Net Force vs Named Forces

    Friction, tension, normal force, and gravity are separate forces. You add them (with signs) to get F_net, then F_net = ma.

    Sliding resistance: friction Ff = μN. Support from a surface:

    normal force N = mg or mg cosθ.

    Circular paths need inward force F = mv²/r — see centripetal force.

    Force, Momentum, and Work

    Impulse links force to momentum change: J = FΔt = Δp. See momentum and p = mv.

    Force through a distance does work: W = Fd. See the work calculator.

    Units

  • m → kg (convert grams first).
  • a → m/s².
  • F → newtons (N).
  • Do not mix weight in newtons with mass in kilograms inside F = ma.

    • Worked Examples

    Example 1: 4.0 kg at 2.5 m/s²

    F = ma = (4.0)(2.5) = 10 N in the direction of acceleration.

    Example 2: find acceleration

    F = 36 N, m = 6.0 kg. a = F/m = 36/6.0 = 6.0 m/s².

    Example 3: find mass

    F = 24 N, a = 3.0 m/s². m = F/a = 24/3.0 = 8.0 kg.

    Example 4: weight

    m = 5.0 kg, g = 9.8 m/s². W = mg = 49 N downward. That is the gravitational force, not a separate “kind” of F = ma.

    Common Mistakes

  • Using grams in F = ma without converting to kilograms.
  • Treating one applied force as F_net when friction or other forces act.
  • Confusing mass (kg) with weight (N).
  • Forgetting that F and a point the same way for the net-force direction.

    • Check It on the Calculator

    Force calculator — F = ma.

    Acceleration calculator.

    Friction calculator.

    Momentum calculator.

    Learn F = ma and confirm every homework number on the calculator.

    Articles

    • How to Calculate Acceleration (a = (v − u)/t)
    • How to Calculate Momentum (p = mv): Impulse & Conservation
    • How to Calculate Equivalent Resistance: Series & Parallel (R₁ + R₂)
    • How to Calculate Power (P = W/t): Work Rate in Watts
    • How to Calculate Friction Force (Ff = μN): Static & Kinetic
    • How to Calculate Work (W = Fd): Force, Distance & Energy

    All articles · Browse all calculators