Engineering Calculator: How to Calculate Force, Power, Torque, and Mechanical Advantage

Engineering calculations form the backbone of modern design and construction. Whether you’re designing a lever system, sizing a motor, calculating gear ratios, or checking if a beam can support a load, knowing how to apply core engineering formulas is essential.

Use the Engineering Calculator on Today Calculator to handle these calculations accurately without manual formula lookups.

Essential Engineering Formulas

Concept	Formula	Units	When to Use
Torque	τ = F × r	N·m	Rotational force on a shaft or lever
Mechanical Advantage	MA = F_out ÷ F_in	Ratio	How much a machine multiplies your force
Stress	σ = F ÷ A	Pa (N/m²)	Load per unit cross-sectional area
Strain	ε = ΔL ÷ L₀	Ratio	Deformation relative to original length
Young’s Modulus	E = σ ÷ ε	Pa	Material stiffness (higher = stiffer)
Power (Rotational)	P = τ × ω	Watts	Motor or engine power at given RPM
Gear Ratio	GR = N₂ ÷ N₁	Ratio	Teeth on driven gear ÷ teeth on driving gear

Real-World Example 1: Torque Wrench Settings

You need to tighten a bolt to 80 N·m of torque. Your wrench is 0.3 meters long. What force do you apply?

τ = F × r → F = τ ÷ r = 80 ÷ 0.3 = 266.7 N (about 60 pounds of force).

Try different lengths and forces on the Engineering Calculator.

Real-World Example 2: Lever Mechanical Advantage

A crowbar is 1 meter long. The fulcrum is 15 cm from the load. What’s the mechanical advantage?

MA = Effort Arm ÷ Load Arm = (100 − 15) ÷ 15 = 85 ÷ 15 = 5.67

That means a 50 N force at the handle creates 50 × 5.67 = 283.5 N at the load end.

Real-World Example 3: Motor Power to Move a Conveyor Belt

A conveyor belt needs to move 200 kg of material 10 meters in 30 seconds. The friction force is 0.15 × weight.

Weight: F = 200 × 9.8 = 1,960 N
Friction: F_friction = 0.15 × 1,960 = 294 N
Work: W = 294 × 10 = 2,940 J
Power: P = 2,940 ÷ 30 = 98 W

A 150 W motor would handle this with a safety margin. Verify this setup on the Engineering Calculator.

Material Property Reference

Material	Young’s Modulus (GPa)	Yield Strength (MPa)	Density (kg/m³)
Structural Steel	200	250	7,850
Aluminum 6061	69	276	2,700
Copper	117	70	8,960
Titanium Grade 5	114	828	4,430
Concrete (compressive)	30	20–40	2,400
Oak Wood (along grain)	11	70	750

Common Engineering Mistakes to Avoid

Forgetting gravity: When calculating force from mass, always multiply by 9.8 m/s² (g)
Mixing units: Don’t combine mm with m, or kg with lb — convert everything to SI first
Ignoring safety factors: Always add a safety margin (typically 1.5–2× calculated values)
Wrong lever arm distance: Torque uses perpendicular distance from pivot to force direction

For all your engineering calculations, use the Engineering Calculator — it handles units, formulas, and gives you results instantly.