Newton's second law – force equals mass times acceleration – is the foundation of classical mechanics. It underlies the jolt when a train pulls away, the force on your body in a car crash and the load an elevator motor must handle. The force calculator solves all three variants of this fundamental formula and shows how force, mass and acceleration relate to each other.
Step by Step: How to Use the Force Calculator
- Choose what to calculate: Do you want to find force (F), mass (m) or acceleration (a)?
- Set the units: Force in Newtons (N), mass in kilograms (kg), acceleration in m/s². For larger forces: kilonewtons (kN) = 1,000 N.
- Enter the known values: Fill in the two known quantities, for example mass 1,500 kg and acceleration 3 m/s².
- Calculate weight force: For gravitational weight force on Earth, use a = g = 9.81 m/s². Simply enter the mass.
- Interpret the result: 1 Newton is the force that accelerates 1 kg at 1 m/s². The weight force of a 1 kg object is 9.81 N.
Practical Examples
Example 1 – Elevator load: An elevator carries 8 passengers at 80 kg each = 640 kg + car weight 600 kg = 1,240 kg total. Weight force: F = 1,240 × 9.81 = 12,164 N = 12.16 kN. The motor must produce at least this force to hold the elevator – plus reserves for upward acceleration.
Example 2 – Car braking: A car (1,800 kg) brakes at a = −8 m/s² (emergency stop). Braking force: F = 1,800 × 8 = 14,400 N = 14.4 kN. This force acts on all four wheels – 3,600 N per tyre. Relevant for brake disc dimensioning.
Example 3 – Crane hook load: A steel beam (mass 3,200 kg) is to be accelerated upward at 0.5 m/s². Required force: F = 3,200 × (9.81 + 0.5) = 3,200 × 10.31 = 32,992 N ≈ 33 kN. The sum of gravitational force and acceleration force gives the actual hook load.
Force Formula: F = m × a
Newton formulas: F = m × a; m = F/a; a = F/m. 1 Newton = 1 kg × 1 m/s². Earth's gravity: g = 9.81 m/s². Weight force: F = m × 9.81. A 70 kg person: F = 686.7 N.
Frequently Asked Questions (FAQ)
What is the difference between weight and mass?
Mass (in kg) is an intrinsic property of an object that never changes. Weight force (in Newtons) is the force gravity exerts on that mass: F = m × g. On the Moon (g = 1.62 m/s²), a 70 kg person has a weight force of only 113.4 N instead of 686.7 N on Earth – but their mass remains 70 kg.
What does "1 kp" (kilopond) mean on old machinery?
The kilopond (kp) is an outdated unit of force: 1 kp = weight force of 1 kg = 9.81 N, approximately 10 N. Old tool data sheets and machine manuals still use kp/cm² (≈ bar) or kN. The calculator can handle this conversion automatically.
How does centripetal force work in rotation?
Centripetal force (directed inward) = m × v² / r or m × ω² × r. It is not an independent "force" in the Newtonian sense, but the force required to keep an object on a circular path. In a washing machine with r = 25 cm and 1,400 rpm: ω = 146.6 rad/s, centripetal force per kg of laundry ≈ 5,370 N – 537 times the gravitational force.
