Free Fall Calculator
Our mechanics calculator computes fall accurately. Enter measurements for results with formulas and error analysis. See charts, tables, and visual results.
Calculator
Adjust values & calculatePositive = thrown downward
Formula
Free fall kinematics: distance fallen equals half of gravitational acceleration times time squared. Velocity equals g times time. These equations assume no air resistance and constant gravitational acceleration. Impact kinetic energy equals half mass times velocity squared.
Last reviewed: December 2025
Worked Examples
Example 1: Dropped Object from Building
Example 2: Free Fall on Mars
Background & Theory
The Free Fall Calculator applies the following established principles and formulas. Physics is the fundamental natural science concerned with matter, energy, and the interactions between them. Classical mechanics, founded on Newton's three laws of motion, provides the framework for analyzing the motion of objects. The first law states that an object remains at rest or in uniform motion unless acted upon by a net external force. The second law quantifies this relationship: F = ma, where force equals mass times acceleration in SI units of newtons (N = kg·m/s²). The third law establishes that every action produces an equal and opposite reaction. Kinematics describes motion without reference to its causes. The four fundamental equations relate displacement s, initial velocity u, final velocity v, acceleration a, and time t: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t. These assume constant acceleration and are foundational for solving projectile motion, free fall, and linear dynamics problems. Energy conservation underpins much of physics. Kinetic energy is KE = ½mv², where m is mass in kilograms and v is speed in meters per second. Gravitational potential energy is PE = mgh, where g ≈ 9.81 m/s² near Earth's surface and h is height in meters. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE. Electricity and circuits rely on Ohm's law: V = IR, where voltage V is in volts, current I in amperes, and resistance R in ohms. Electrical power is P = IV = I²R = V²/R, measured in watts. Wave mechanics connects frequency f, wave speed v, and wavelength λ through f = v/λ, with frequency in hertz (Hz). Pressure is defined as force per unit area, P = F/A, in pascals (Pa = N/m²). The ideal gas law PV = nRT links pressure, volume, moles n, the gas constant R = 8.314 J/(mol·K), and absolute temperature in kelvin. Gravitational force between two masses follows Newton's law of universal gravitation: F = Gm₁m₂/r², where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant.
History
The history behind the Free Fall Calculator traces back through the following developments. The history of physics spans over two millennia, beginning with the natural philosophy of ancient Greece. Aristotle (384–322 BCE) proposed that all matter consisted of four elements and that objects moved toward their natural place, with heavier objects falling faster than lighter ones. While largely incorrect, his systematic approach to explaining nature dominated Western thought for nearly 2,000 years. The Scientific Revolution overturned Aristotelian physics. Galileo Galilei (1564–1642) performed groundbreaking experiments on inclined planes and falling bodies, demonstrating that all objects fall with the same acceleration regardless of mass, and established the principle of inertia. His use of mathematics to describe motion was revolutionary. Isaac Newton synthesized these developments in his landmark Principia Mathematica (1687), laying out the three laws of motion and the law of universal gravitation. Newton's framework unified terrestrial and celestial mechanics, explaining planetary orbits with the same equations governing a falling apple. His calculus provided the mathematical language for expressing rates of change. The 19th century brought two major theoretical achievements. James Clerk Maxwell formulated his equations of electromagnetism between 1861 and 1862, unifying electricity, magnetism, and optics, and predicting the existence of electromagnetic waves traveling at the speed of light. Thermodynamics was developed by Carnot, Clausius, and Kelvin, establishing the laws governing heat, work, and entropy. The 20th century produced two revolutions that fundamentally altered the classical picture. Albert Einstein published the special theory of relativity in 1905, showing that space and time are not absolute but relative to the observer, and that mass and energy are equivalent via E = mc². His general theory of relativity in 1915 reinterpreted gravity as the curvature of spacetime. Simultaneously, quantum mechanics emerged from the work of Planck, Bohr, Heisenberg, and Schrödinger, revealing that at atomic scales energy is quantized and particles exhibit wave-particle duality. These developments culminated in the Standard Model of particle physics, which describes all known fundamental particles and three of the four fundamental forces.
Frequently Asked Questions
Formula
h = ½gt² | v = gt | v² = 2gh | KE = ½mv²
Free fall kinematics: distance fallen equals half of gravitational acceleration times time squared. Velocity equals g times time. These equations assume no air resistance and constant gravitational acceleration. Impact kinetic energy equals half mass times velocity squared.
Worked Examples
Example 1: Dropped Object from Building
Problem: A ball is dropped from the top of a 50m building on Earth. How long does it take to hit the ground, and what is the impact velocity? The ball has mass 0.5 kg.
Solution: h = 50m, v₀ = 0, g = 9.81 m/s²\nFall time: t = √(2h/g) = √(100/9.81) = 3.193 s\nImpact velocity: v = gt = 9.81 × 3.193 = 31.32 m/s\nConverted: 31.32 × 3.6 = 112.8 km/h\nKinetic energy: KE = ½mv² = 0.5 × 0.5 × 31.32² = 245.2 J\nPotential energy: PE = mgh = 0.5 × 9.81 × 50 = 245.3 J ✓
Result: t = 3.19s | v = 31.3 m/s (112.8 km/h) | KE = 245.2J
Example 2: Free Fall on Mars
Problem: How far does an object fall in 5 seconds on Mars (g = 3.72 m/s²) if thrown downward at 2 m/s?
Solution: t = 5s, v₀ = 2 m/s, g = 3.72 m/s²\nDistance: d = v₀t + ½gt² = 2×5 + 0.5×3.72×25 = 10 + 46.5 = 56.5m\nFinal velocity: v = v₀ + gt = 2 + 3.72×5 = 20.6 m/s\nConverted: 20.6 × 3.6 = 74.2 km/h
Result: d = 56.5m | v = 20.6 m/s (74.2 km/h)
Frequently Asked Questions
What is free fall?
Free fall is the motion of an object falling under the sole influence of gravity, with no air resistance or other forces acting on it. In free fall, all objects accelerate at the same rate regardless of mass — this was famously demonstrated by Galileo and later confirmed by Apollo 15 astronauts dropping a hammer and feather on the Moon. On Earth, free fall acceleration (g) is approximately 9.81 m/s² (32.2 ft/s²). The basic kinematic equations are: distance = ½gt², velocity = gt, and v² = 2gh (for objects starting from rest). Free fall is an idealization; real falling objects experience air resistance.
How do you calculate fall time from height?
For an object dropped from rest (v₀ = 0) from height h: Time = √(2h/g). For example, dropping from 100m on Earth: t = √(2×100/9.81) = √20.39 = 4.52 seconds. With an initial downward velocity v₀: use the quadratic formula on h = v₀t + ½gt², giving t = [-v₀ + √(v₀² + 2gh)] / g. Common fall times on Earth: 1 second = 4.9m, 2 seconds = 19.6m, 3 seconds = 44.1m, 5 seconds = 122.6m, 10 seconds = 490.5m.
What is the difference between free fall and terminal velocity?
Free fall assumes no air resistance — the object continuously accelerates at g. In reality, air resistance (drag) increases with speed. Terminal velocity is reached when drag force equals gravitational force, so acceleration becomes zero and speed remains constant. Terminal velocities vary greatly: skydiver (belly-down) ≈ 53 m/s (190 km/h), skydiver (head-down) ≈ 90 m/s (320 km/h), baseball ≈ 42 m/s (150 km/h), tennis ball ≈ 31 m/s (110 km/h), raindrop ≈ 9 m/s (32 km/h). Free fall calculations are accurate for short falls, dense objects, or vacuum conditions.
How accurate are the results from Free Fall Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy