Engineering Calculator: How to Calculate Beam Deflection, Stress, and Gear Ratios

Engineering calculations span four domains — structural, electrical, mechanical, and materials — and each has its own formulas for deflection, stress, power, and efficiency. The Engineering Calculator at Today Calculator bundles the most-used professional formulas into one tool, so you can check beam deflection, sizing, and drive-system numbers without flipping through a handbook.

Structural Engineering: Beams, Stress, and Buckling

The structural section handles the three calculations that come up most often when sizing beams and columns:

Calculation	Formula	When You Need It
Simply supported beam deflection	δ = (5wL⁴)/(384EI) for distributed loads, (PL³)/(48EI) for point loads	Checking whether a beam sags too far under load
Stress	σ = F/A (normal), τ = F/A (shear)	Verifying a member won’t yield under applied force
Column buckling (Euler)	P_cr = (π²EI)/(KL)²	Finding the critical load before a slender column buckles
Moment of inertia	I = ∫y²dA (rectangle, circle, I-beam presets)	Input for deflection and buckling formulas

Worked example: a simply supported beam with a distributed load of 2,000 N/m over 4 m, E = 200 GPa, I = 8 × 10⁻⁶ m⁴. Deflection δ = (5 × 2000 × 4⁴)/(384 × 200e9 × 8e-6) ≈ 0.0042 m, or about 4.2 mm — comfortably within most span/360 limits.

Electrical Engineering: Power and Motor Analysis

The electrical section covers AC power, motor efficiency, cable voltage drop, and transformer ratios:

• AC power: P = VI cos(φ) for real power, Q = VI sin(φ) for reactive power, S = VI for apparent power.
• Motor efficiency: η = P_out/P_in × 100% — a motor drawing 5 kW input and delivering 4.2 kW output is 84% efficient.
• Voltage drop: V_drop = I × R × L × 2 for a round-trip cable run — keep it under 3% for lighting circuits.
• Transformer: V₂/V₁ = N₂/N₁ and I₂/I₁ = N₁/N₂ — step-up and step-down ratios in one view.

Mechanical Engineering: Gears, Belts, and Power Transmission

For drive systems, the mechanical section gives you gear ratio and belt drive calculations:

• Gear ratio: GR = N₂/N₁ — a 40-tooth driven gear on a 20-tooth driver gives a 2:1 ratio, doubling torque and halving speed.
• Belt drive: v = πDN/60 for belt speed, T = P/ω for torque from power — use pulley diameters and RPM to match speeds between shafts.

Example: a driver pulley of 0.1 m diameter at 1,500 RPM drives a 0.2 m driven pulley. Belt speed v = π × 0.1 × 1500/60 ≈ 7.85 m/s, and the driven pulley turns at 750 RPM — a 2:1 speed reduction.

Materials Engineering Section

The materials tab rounds out the tool with calculations for material properties — density, stress-strain relationships, and section properties — so you can compare candidates (steel vs aluminum vs composites) before committing to a design.

Whether you are checking a beam for a home renovation, sizing a motor, or verifying a gearbox design, the Engineering Calculator gives you professional-grade results with step-by-step solutions — no handbook required.