How to calculate a torque?

Three common cases. (1) From horsepower and shaft speed: T = 5252 × HP / RPM (lb·ft) or T = 9549 × kW / RPM (N·m). (2) From force and lever arm: T = F × r × sin θ, where r is the perpendicular distance from the rotation axis. (3) From measured power input: T = P_shaft / ω, where ω = 2π·N/60. The RPM calculator handles cases 1 and 3 automatically.

How do i calculate current?

For a DC or single-phase resistive circuit: I = V / R (Ohm's Law) or I = P / V (Power Law). For a single-phase AC circuit with reactive load: I = P / (V × PF). For a three-phase circuit: I = P × 1000 / (√3 × V × PF) where P is in kW. The power calculator handles every variant in one form.

How to calculate current in a parallel circuit?

In a parallel circuit, branch voltages are equal and branch currents add: I_total = I₁ + I₂ + … + I_n, where each branch current is I_i = V / R_i (Ohm's Law per branch). For complex impedances in AC: I_total = V × Σ(1 / Z_i). The parallel-circuits reference page covers the full algebra.

How to calculate drag coefficient?

C_d = 2 × F_d / (ρ × V² × A), where F_d is the measured drag force in newtons, ρ is the fluid density (1.225 kg/m³ for air at sea level, 1000 kg/m³ for water), V is the relative velocity in m/s, and A is the reference area (frontal area for cars, wing planform for aircraft). C_d is dimensionless. Typical values: smooth sphere 0.47, modern car 0.25–0.30, cyclist tucked 0.5, parachute 1.4.

How to calculate the drag coefficient?

Same formula as above — C_d = 2 × F_d / (ρ × V² × A). Either measure F_d directly in a wind tunnel, or back-compute from the terminal velocity of a falling object: at terminal velocity, gravity = drag, so m·g = ½·ρ·V_term²·A·C_d → C_d = 2·m·g / (ρ·V_term²·A). Used heavily in aerospace, automotive, and bicycle design.

How to calculate coefficient of drag?

Same answer as above — C_d = 2 × F_d / (ρ × V² × A). The three names (drag coefficient, "the drag coefficient", "coefficient of drag") all describe the same dimensionless ratio. Use SI units consistently: F_d in newtons, ρ in kg/m³, V in m/s, A in m². The result is unitless.

How to calculate rpm?

For an AC induction motor at synchronous speed: RPM = 120 × f / P, where f is supply frequency (Hz) and P is the number of poles. Loaded RPM is slightly lower because of slip: N = N_synchronous × (1 − s), with s ≈ 0.02–0.05 for NEMA Design B. For belt / pulley drives: N₂ = N₁ × D₁ / D₂. The RPM calculator covers both cases.

How do i calculate rpm?

Same as above. For a 4-pole 60 Hz motor: synchronous = 1800 RPM, loaded ≈ 1750–1780 RPM. For 60 Hz motors: 2-pole = 3600 sync (≈ 3450 loaded); 4-pole = 1800 sync; 6-pole = 1200 sync; 8-pole = 900 sync. The RPM page tabulates the full ladder.

How to calculate refraction angle?

Snell's law: n₁ × sin(θ₁) = n₂ × sin(θ₂). Solve for θ₂: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Indices of refraction: vacuum / air ≈ 1.0; water 1.33; common glass 1.5; diamond 2.42. Light entering a denser medium bends toward the normal (smaller angle); entering a less-dense medium bends away. Total internal reflection at θ₁ > arcsin(n₂ / n₁).

How to calculate the angle of refraction?

Same Snell's law: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Worked example: light in air (n = 1.0) hitting water surface (n = 1.33) at 30° from normal → θ₂ = arcsin((1.0 / 1.33) × sin 30°) = arcsin(0.376) = 22.1° from normal in water. The light bends toward the normal as it enters the denser medium.

How to calculate a torque?

Three common cases. (1) From horsepower and shaft speed: T = 5252 × HP / RPM (lb·ft) or T = 9549 × kW / RPM (N·m). (2) From force and lever arm: T = F × r × sin θ, where r is the perpendicular distance from the rotation axis. (3) From measured power input: T = P_shaft / ω, where ω = 2π·N/60. The RPM calculator handles cases 1 and 3 automatically.

How do i calculate current?

For a DC or single-phase resistive circuit: I = V / R (Ohm's Law) or I = P / V (Power Law). For a single-phase AC circuit with reactive load: I = P / (V × PF). For a three-phase circuit: I = P × 1000 / (√3 × V × PF) where P is in kW. The power calculator handles every variant in one form.

How to calculate current in a parallel circuit?

In a parallel circuit, branch voltages are equal and branch currents add: I_total = I₁ + I₂ + … + I_n, where each branch current is I_i = V / R_i (Ohm's Law per branch). For complex impedances in AC: I_total = V × Σ(1 / Z_i). The parallel-circuits reference page covers the full algebra.

How to calculate drag coefficient?

C_d = 2 × F_d / (ρ × V² × A), where F_d is the measured drag force in newtons, ρ is the fluid density (1.225 kg/m³ for air at sea level, 1000 kg/m³ for water), V is the relative velocity in m/s, and A is the reference area (frontal area for cars, wing planform for aircraft). C_d is dimensionless. Typical values: smooth sphere 0.47, modern car 0.25–0.30, cyclist tucked 0.5, parachute 1.4.

How to calculate the drag coefficient?

Same formula as above — C_d = 2 × F_d / (ρ × V² × A). Either measure F_d directly in a wind tunnel, or back-compute from the terminal velocity of a falling object: at terminal velocity, gravity = drag, so m·g = ½·ρ·V_term²·A·C_d → C_d = 2·m·g / (ρ·V_term²·A). Used heavily in aerospace, automotive, and bicycle design.

How to calculate coefficient of drag?

Same answer as above — C_d = 2 × F_d / (ρ × V² × A). The three names (drag coefficient, "the drag coefficient", "coefficient of drag") all describe the same dimensionless ratio. Use SI units consistently: F_d in newtons, ρ in kg/m³, V in m/s, A in m². The result is unitless.

How to calculate rpm?

For an AC induction motor at synchronous speed: RPM = 120 × f / P, where f is supply frequency (Hz) and P is the number of poles. Loaded RPM is slightly lower because of slip: N = N_synchronous × (1 − s), with s ≈ 0.02–0.05 for NEMA Design B. For belt / pulley drives: N₂ = N₁ × D₁ / D₂. The RPM calculator covers both cases.

How do i calculate rpm?

Same as above. For a 4-pole 60 Hz motor: synchronous = 1800 RPM, loaded ≈ 1750–1780 RPM. For 60 Hz motors: 2-pole = 3600 sync (≈ 3450 loaded); 4-pole = 1800 sync; 6-pole = 1200 sync; 8-pole = 900 sync. The RPM page tabulates the full ladder.

How to calculate refraction angle?

Snell's law: n₁ × sin(θ₁) = n₂ × sin(θ₂). Solve for θ₂: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Indices of refraction: vacuum / air ≈ 1.0; water 1.33; common glass 1.5; diamond 2.42. Light entering a denser medium bends toward the normal (smaller angle); entering a less-dense medium bends away. Total internal reflection at θ₁ > arcsin(n₂ / n₁).

How to calculate the angle of refraction?

Same Snell's law: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Worked example: light in air (n = 1.0) hitting water surface (n = 1.33) at 30° from normal → θ₂ = arcsin((1.0 / 1.33) × sin 30°) = arcsin(0.376) = 22.1° from normal in water. The light bends toward the normal as it enters the denser medium.

Reference · Aggregate · Calculation hub · Cross-discipline

How to Calculate — Engineering Reference Hub

"How to calculate X" is the most-asked engineering question on the internet. This aggregate page indexes the canonical formulas for the dozen highest-volume calculations — current, torque, RPM, kVA, drag coefficient, refraction angle, road-base aggregate volume, orbital period — and links each to its dedicated this calculator. Reviewed by a licensed PE.

Calculator hub — pick the dedicated tool

For every "how to calculate X" question below, the site has a dedicated calculator that returns numerical output and (for the electrical family) NEC-compliant conductor sizing. Use this page as the cross-reference; jump to the dedicated calculator for the actual computation.

→ Power (V, I, P, R) · → Three-phase power · → RPM / speed · → Voltage drop · → Wire size · → Moment of inertia · → Truss

Canonical formulas — one card per quantity

Eq. 01 — Current (Ohm and Power Laws) SI

I = \frac{V}{R} = \frac{P}{V} = \frac{P}{V \cdot PF} \text{ (1-phase AC)}

·: I = current in amperes
·: V = voltage; R = resistance; P = real power; PF = power factor
·: For 3-phase: I = P × 1000 / (√3 × V × PF), P in kW

Eq. 02 — Torque from horsepower and RPM SI

T = \frac{5252 \cdot HP}{N}

·: T = shaft torque (lb·ft)
·: HP = horsepower; N = RPM
·: Metric: T (N·m) = 9549 × kW / RPM

Eq. 03 — Synchronous RPM SI

N_s = \frac{120 \cdot f}{P}

·: N_s = synchronous speed (RPM)
·: f = supply frequency (50 or 60 Hz)
·: P = number of motor poles

Eq. 04 — Drag coefficient SI

C_d = \frac{2 F_d}{\rho V^2 A}

·: F_d = drag force (N)
·: ρ = fluid density (1.225 kg/m³ air; 1000 kg/m³ water)
·: V = velocity (m/s); A = reference area (m²)

Eq. 05 — Snell's law (angle of refraction) SI

n_1 \sin \theta_1 = n_2 \sin \theta_2

·: n₁, n₂ = indices of refraction (air 1.0, water 1.33, glass 1.5)
·: θ₁, θ₂ = angles measured from the surface normal
·: Total internal reflection when sin θ₁ > n₂ / n₁

Eq. 06 — Orbital period (Kepler's third law) SI

T = 2\pi \sqrt{\frac{a^3}{G M}}

·: T = orbital period (s)
·: a = semi-major axis (m)
·: G = 6.674 × 10⁻¹¹ m³/(kg·s²); M = primary body mass (kg)

Eq. 07 — Road-base aggregate volume SI

V_{aggregate} = L \cdot W \cdot D \cdot c_f

·: L, W, D = length, width, compacted depth (m)
·: c_f = compaction factor (1.20–1.40 for crushed stone)
·: Convert to tons: V × 1.5–1.7 t/m³ depending on aggregate density

Standards by calculation family

Family	Primary standard
Electrical (current, power, voltage drop)	NEC (NFPA 70), IEEE 141, IEC 60364
Motor (RPM, torque, FLA)	NEMA MG 1, IEEE 112, IEC 60034
Structural (moment, truss, deflection)	AISC 360, ASCE 7, ACI 318, EN 1993
Fluid mechanics (drag, head loss)	ASME PTC, ASHRAE Handbook
Optical (refraction)	ISO 10110, ANSI Z80.36
Aggregate / civil (road base, concrete)	AASHTO M147, ACI 211, FHWA standards
Orbital mechanics	NASA Standard 4-1A, ISO 27852 (orbital lifetime)

Identify the quantity to calculate Pick from the master list — current, torque, RPM, kVA, kW, voltage drop, drag coefficient, refraction angle, road-base aggregate volume, orbital period. Each has its own formula, units, and standard reference.
Look up the canonical formula Each calculation has one or two canonical equations. Current: I = V/R or I = P/V. Torque: T = 5252·HP/RPM. RPM: N = 120·f/P. Drag coefficient: Cd = 2·F_d / (ρ·V²·A). Refraction: n₁·sin(θ₁) = n₂·sin(θ₂). Always cite the source standard (NEC, NEMA, IEEE, AISC, IBC, ASCE, NIST).
Substitute units carefully Engineering practice uses mixed unit systems. North American electrical: V, A, Ω, kW, HP. Metric structural: m, mm, kN, MPa. Always write units beside every value and cancel them as you go — dimensional analysis catches 80 % of arithmetic errors.
Apply code or design factors NEC §210.20 — multiply continuous loads by 1.25. AISC LRFD — multiply by load factors (1.2 D + 1.6 L) and divide by resistance factor φ. ASD — divide by safety factor Ω. ASCE 7 — apply importance factor I, gust factor G, exposure category D/C/B.
Verify with the dedicated calculator The library has dedicated calculators for the most-asked quantities — power, three-phase power, voltage drop, wire size, RPM, torque, moment of inertia, truss analysis. Use the dedicated tool when you need PDF output or NEC-compliant conductor selection.

Worked example — 3-phase motor branch ampacity

Calculate the conductor ampacity for a 50 HP 480 V three-phase motor.

FLA from NEC Table 430.250: 65 A.
Required ampacity: 1.25 × 65 = 81.25 A (NEC §430.22).
Wire size (NEC 310.16, 75 °C copper): 4 AWG (85 A) — meets the demand.
Branch overcurrent (NEC §430.52, inverse-time breaker): 2.50 × 65 = 162.5 A → 175 A (next standard).

Comparison — manual calculation vs. dedicated calculator

Approach	Strengths	Weaknesses
Pencil-and-paper	Builds intuition; no dependence on software	Slow; arithmetic-error prone; no PDF output
Spreadsheet	Reproducible, auditable, custom formulas	Each engineer rebuilds same logic; version drift
Dedicated web calculator (the site)	NEC / NEMA / AISC built-in; PDF export; mobile-friendly	Black-box if you don\'t read the underlying engine
CAD / FEA software (Revit, ETAP, SAP2000)	Full project context, BIM linkage	Cost, training, overkill for spot calculations

Variants and absorbed sub-clusters

Calculate torque (motor and shaft applications)

Beyond the basic T = 5252·HP/RPM, motor torque has nuance: starting torque (NEMA Design B ≈ 150 % of rated), pull-out torque (≈ 200 %), breakdown torque (≈ 220 %), locked-rotor torque. For belt drives, T₂ = T₁ × N₁/N₂ (inverse of speed ratio). The RPM calculator outputs both rated and starting torque from nameplate inputs.

Calculate current — DC, AC, three-phase

DC: I = V/R or P/V. Single-phase AC with reactive load: I = P / (V × PF). Three-phase: I = P × 1000 / (√3 × V × PF). For motor branches, always cross-check with NEC Table 430.250 FLA — the table value supersedes computed I for sizing breakers and conductors per NEC §430.6.

Calculate phase (3-phase angle and sequence)

For a balanced 3-phase system, voltages are 120° apart. To compute phase from line quantities: V_phase = V_line / √3 in wye; V_phase = V_line in delta. Phase rotation (ABC vs. ACB) determines motor direction and is verified with a phase-rotation tester before commissioning.

Calculate RPM (motor synchronous and slip)

N_s = 120·f/P gives synchronous RPM. Loaded RPM is N = N_s × (1 − s), with s ≈ 0.02–0.05 for NEMA Design B at full load. Common 60 Hz machines: 2-pole = 3600 sync, 4-pole = 1800, 6-pole = 1200, 8-pole = 900.

Calculate load (electrical and structural)

Electrical: NEC Article 220 builds load using general lighting × demand factor + appliance loads + largest motor × 1.25. Structural: ASCE 7 dead + live + roof + snow + wind + seismic combinations per Chapter 2. Both result in a single design value to size conductors / members.

Calculate density and specific gravity

Density: ρ = m / V. Specific gravity: SG = ρ_substance / ρ_water (water = 1000 kg/m³). Petroleum specific gravity uses the API formula API = (141.5 / SG) − 131.5. The site specific-gravity reference tabulates 25 common substances.

Calculate orbital period (Kepler\'s third law)

T = 2π × √(a³ / GM). For Earth orbit: T (minutes) ≈ 84.49 × (a / R_earth)^1.5 where R_earth = 6 378 km. ISS at 408 km altitude (a = 6 786 km): T = 92.7 minutes. GEO at 35 786 km altitude: T = 1 436 minutes (sidereal day).

Calculate road base aggregate volume

V = L × W × D × c_f, where c_f is the compaction factor (1.20–1.40 for crushed stone base). Convert to tons by multiplying volume in m³ by aggregate density (1.5–1.7 t/m³). For a 30-m × 4-m × 0.20-m road base at c_f = 1.30: 30 × 4 × 0.20 × 1.30 = 31.2 m³ = ~50 tons.

Frequently asked questions

How to calculate a torque?: Three common cases. (1) From horsepower and shaft speed: T = 5252 × HP / RPM (lb·ft) or T = 9549 × kW / RPM (N·m). (2) From force and lever arm: T = F × r × sin θ, where r is the perpendicular distance from the rotation axis. (3) From measured power input: T = P_shaft / ω, where ω = 2π·N/60. The RPM calculator handles cases 1 and 3 automatically.
How do i calculate current?: For a DC or single-phase resistive circuit: I = V / R (Ohm's Law) or I = P / V (Power Law). For a single-phase AC circuit with reactive load: I = P / (V × PF). For a three-phase circuit: I = P × 1000 / (√3 × V × PF) where P is in kW. The power calculator handles every variant in one form.
How to calculate current in a parallel circuit?: In a parallel circuit, branch voltages are equal and branch currents add: I_total = I₁ + I₂ + … + I_n, where each branch current is I_i = V / R_i (Ohm's Law per branch). For complex impedances in AC: I_total = V × Σ(1 / Z_i). The parallel-circuits reference page covers the full algebra.
How to calculate drag coefficient?: C_d = 2 × F_d / (ρ × V² × A), where F_d is the measured drag force in newtons, ρ is the fluid density (1.225 kg/m³ for air at sea level, 1000 kg/m³ for water), V is the relative velocity in m/s, and A is the reference area (frontal area for cars, wing planform for aircraft). C_d is dimensionless. Typical values: smooth sphere 0.47, modern car 0.25–0.30, cyclist tucked 0.5, parachute 1.4.
How to calculate the drag coefficient?: Same formula as above — C_d = 2 × F_d / (ρ × V² × A). Either measure F_d directly in a wind tunnel, or back-compute from the terminal velocity of a falling object: at terminal velocity, gravity = drag, so m·g = ½·ρ·V_term²·A·C_d → C_d = 2·m·g / (ρ·V_term²·A). Used heavily in aerospace, automotive, and bicycle design.
How to calculate coefficient of drag?: Same answer as above — C_d = 2 × F_d / (ρ × V² × A). The three names (drag coefficient, "the drag coefficient", "coefficient of drag") all describe the same dimensionless ratio. Use SI units consistently: F_d in newtons, ρ in kg/m³, V in m/s, A in m². The result is unitless.
How to calculate rpm?: For an AC induction motor at synchronous speed: RPM = 120 × f / P, where f is supply frequency (Hz) and P is the number of poles. Loaded RPM is slightly lower because of slip: N = N_synchronous × (1 − s), with s ≈ 0.02–0.05 for NEMA Design B. For belt / pulley drives: N₂ = N₁ × D₁ / D₂. The RPM calculator covers both cases.
How do i calculate rpm?: Same as above. For a 4-pole 60 Hz motor: synchronous = 1800 RPM, loaded ≈ 1750–1780 RPM. For 60 Hz motors: 2-pole = 3600 sync (≈ 3450 loaded); 4-pole = 1800 sync; 6-pole = 1200 sync; 8-pole = 900 sync. The RPM page tabulates the full ladder.
How to calculate refraction angle?: Snell's law: n₁ × sin(θ₁) = n₂ × sin(θ₂). Solve for θ₂: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Indices of refraction: vacuum / air ≈ 1.0; water 1.33; common glass 1.5; diamond 2.42. Light entering a denser medium bends toward the normal (smaller angle); entering a less-dense medium bends away. Total internal reflection at θ₁ > arcsin(n₂ / n₁).
How to calculate the angle of refraction?: Same Snell's law: θ₂ = arcsin((n₁ / n₂) × sin θ₁). Worked example: light in air (n = 1.0) hitting water surface (n = 1.33) at 30° from normal → θ₂ = arcsin((1.0 / 1.33) × sin 30°) = arcsin(0.376) = 22.1° from normal in water. The light bends toward the normal as it enters the denser medium.

Historic source — the equations of electromagnetism

Maxwell\'s 1873 treatise consolidated centuries of separate empirical results — Coulomb, Ampère, Faraday, Gauss — into the four field equations that govern every modern electrical calculation. Every "how to calculate" question in electrical engineering reduces to one of these four.

James Clerk Maxwell — A Treatise on Electricity and Magnetism → Vol. II, 1873 — the four equations that unified all of electromagnetic calculation

Related calculators and references

Sources and further reading

NFPA 70 — National Electrical Code (current edition).
NEMA MG 1 — Motors and Generators (current edition).
AISC 360-22 — Specification for Structural Steel Buildings.
ASCE 7-22 — Minimum Design Loads and Associated Criteria.
AASHTO M147 — Standard Specification for Materials for Aggregate and Soil-Aggregate Subbase, Base, and Surface Courses.
Maxwell, J. C. A Treatise on Electricity and Magnetism. Oxford, 1873.