Greatest Common Divisor Calculator

A physics calculator applies fundamental equations from classical mechanics, thermodynamics, fluid dynamics, and materials science to compute unknown quantities from known inputs. Physics formulas relate physical quantities — force, mass, acceleration, velocity, pressure, energy, temperature — through well-established mathematical relationships derived from physical laws. Engineering applications of these formulas underpin structural design, mechanical systems, fluid handling, heat transfer, and electrical systems. and provide related engineering calculation tools.

The key to applying physics formulas correctly is dimensional analysis — ensuring that the units on both sides of an equation are consistent. SI units (metres, kilograms, seconds, newtons, pascals, joules, watts) are the international standard for engineering calculations. Converting all inputs to SI units before calculating, then converting the result to the required output unit, eliminates the most common source of physics calculation errors.

1. Identify the physical quantity you want to calculate (force, velocity, pressure, torque, etc.).
2. Select the appropriate formula and identify which variables are known and which is unknown.
3. Convert all inputs to consistent SI units before entering values.
4. Enter the known values — the calculator solves for the target quantity.
5. Check the result against physical intuition — an order-of-magnitude sanity check catches unit errors.
6. Convert the result to required output units if needed.

Core physics and engineering formulas

Newton's second law: F = ma (Force = mass × acceleration)

Speed: v = d/t (velocity = distance ÷ time)

Kinetic energy: KE = ½mv² (mass × velocity²)

Potential energy: PE = mgh (mass × gravity × height)

Power: P = W/t = F × v (work per unit time)

Pressure: P = F/A (force per unit area)

Torque: T = F × r (force × lever arm distance)

Stress: σ = F/A (force per cross-sectional area)

Flow rate: Q = v × A (velocity × cross-sectional area)

Heat transfer: Q = ṁ × Cp × ΔT (mass flow × specific heat × temperature difference)

Engineering physics calculation context

SI unit reference

Key SI units for engineering: Force — Newton (N = kg·m/s²); Pressure/Stress — Pascal (Pa = N/m²); Energy — Joule (J = N·m); Power — Watt (W = J/s); Torque — Newton-metre (N·m); Flow rate — cubic metres per second (m³/s); Temperature — Kelvin (K) or Celsius (°C for differences). Common conversions: 1 bar = 100,000 Pa; 1 MPa = 1 N/mm² (useful for material stress); 1 kW = 1,000 W; 1 litre/second = 0.001 m³/s. Engineering safety factors typically require calculated values to be divided by a safety factor of 1.5–4× before use in design.

Math tips and best practices

• Always perform dimensional analysis — write the units alongside each quantity and cancel them through the formula to verify the result has the correct units.
• Apply safety factors to engineering calculations — calculated values represent theoretical limits; real designs include a safety factor of 1.5–4× depending on the application and consequences of failure.
• For fluid flow, check whether the flow is laminar (Re < 2300) or turbulent (Re > 4000) — the Reynolds number determines which flow equations apply.
• Material properties (Young's modulus, yield strength, thermal conductivity) vary with temperature — use values at the operating temperature, not ambient values, for high-temperature applications.

• Structural steel has a yield strength of approximately 250–355 MPa — meaning it can withstand 250–355 N per mm² of cross-sectional area before permanent deformation.
• Water at 20°C has a density of 998 kg/m³ and dynamic viscosity of 1.002 mPa·s — standard reference values for hydraulic and fluid engineering calculations.
• The speed of sound in air at 20°C is approximately 343 m/s; in steel approximately 5,960 m/s — relevant for vibration, acoustics, and non-destructive testing applications.
• A safety factor of 2.0 means the design can theoretically withstand twice the maximum expected load before failure — common in static structural applications.

Common mistakes to avoid

• Mixing unit systems — using pounds (force) with kilograms (mass) produces errors; always convert entirely to SI or entirely to imperial before calculating.
• Forgetting the safety factor — calculated theoretical values are not safe design values; always apply appropriate safety factors per applicable engineering standards.
• Using gauge pressure instead of absolute pressure — fluid mechanics equations require absolute pressure; gauge pressure = absolute − atmospheric (101,325 Pa).
• Ignoring dynamic effects in static formulas — impact loads, vibration, and fatigue cycling require more conservative factors than simple static load calculations.

Engineering calculations that affect structural integrity, pressure systems, electrical installations, or other safety-critical applications must be carried out or reviewed by a chartered or licensed engineer in accordance with applicable codes and standards (BS EN Eurocodes, ASME, ISO, IEC, and national equivalents). This calculator provides educational estimates only and does not constitute professional engineering advice. Safety-critical design calculations must comply with all applicable standards and regulations.