Force is the push or pull that changes an object’s state of motion. This calculator applies Newton’s second law — F = m × a — and solves for whichever of the three variables you do not know. It handles a full range of real-world units (newtons, kilonewtons, pound-force, kilograms-force, grams, pounds, slugs, g-forces, and more), converts everything to SI internally, and displays the step-by-step working so you can follow or verify every calculation.
Whether you are completing a physics homework problem, estimating the thrust needed for a model rocket, checking the braking force on a vehicle, or converting between imperial and metric force units, this tool covers the calculation end-to-end.
The formula and its three forms
Newton’s second law relates force, mass, and acceleration in one equation:
F = m × a
Rearranged to isolate each variable:
| Solving for | Formula | When to use |
|---|---|---|
| Force F | F = m × a | You know what’s moving (mass) and how fast it’s speeding up (acceleration). |
| Mass m | m = F ÷ a | You know the applied force and the resulting acceleration. |
| Acceleration a | a = F ÷ m | You know the force and the mass; you want the resulting acceleration. |
The SI units lock together neatly: one newton (N) is exactly 1 kg·m/s². That means if you enter mass in kilograms and acceleration in m/s² the result is newtons with no conversion factor needed.
How it works
- You choose which variable to solve for using the dropdown.
- You enter the other two values, each with its own unit selector.
- The tool multiplies or divides by the appropriate conversion factor to bring every input into SI (kg, m/s², N), performs the arithmetic, then converts the result back into whichever display unit you choose.
- A summary table always shows all three quantities in SI alongside useful equivalents (kilograms-force, pound-mass, g-force).
- The “Show working” panel reproduces every step — unit conversion, substitution, and the final arithmetic — so nothing is a black box.
Worked example
A 1,200 kg car brakes and decelerates at 8 m/s². What braking force is required?
- Formula: F = m × a
- Inputs: m = 1,200 kg, a = 8 m/s²
- F = 1,200 × 8 = 9,600 N = 9.6 kN
As a sense-check: the weight of the car is 1,200 × 9.80665 = 11,768 N, so the braking force is about 82% of the car’s weight — a hard but plausible stop.
| Scenario | m | a | F |
|---|---|---|---|
| Braking car | 1,200 kg | 8 m/s² | 9,600 N |
| Person falling | 70 kg | 9.80665 m/s² (1 g) | 686.5 N |
| Space capsule re-entry (4 g) | 5,000 kg | 39.2 m/s² | 196 kN |
| Table-tennis ball served | 2.7 g | 2,000 m/s² | 5.4 N |
Units and constants used
- Standard gravity: g = 9.80665 m/s² (exact SI definition)
- 1 pound-force (lbf): 4.44822 N
- 1 kilogram-force (kgf): 9.80665 N
- 1 dyne: 10⁻⁵ N
- 1 slug: 14.5939 kg (FPS unit of mass; 1 slug × 1 ft/s² = 1 lbf)
All figures are calculated in your browser — no data is ever uploaded.