Inductors Formulas
Inductor formulas govern stored magnetic energy, reactance, and the transient response of RL circuits. These calculators let you size inductors for filters, converters, and energy storage, and predict how current ramps over time. They are indispensable when designing switching regulators and EMI suppression networks.
Inductors Formula Calculators
- Inductive Reactance XL = 2πfL Frequency 100 Hz, Inductance 100 µH → Reactance = 62.83 mΩ
- RL Time Constant τ = L / R Inductance 100 µH, Resistance 1 Ω → Time Constant = 100 µs
- Inductor Energy E = ½LI² Inductance 100 µH, Current 2 mA → Energy = 2 × 10⁻⁴ µJ
- Series Inductance Ltotal = L1 + L2 + ... + Ln Inductor Values 100 µH, 0.22 mH, 0.47 mH → Ltotal = 0.79 mH
- Parallel Inductance 1/Ltotal = 1/L1 + 1/L2 + ... + 1/Ln Inductor Values 100 µH, 0.22 mH, 0.47 mH → 1/Ltotal = 6 × 10⁻⁵
- Inductor Quality Factor Q = 2πfL / Rdc Frequency 100 kHz, Inductance 100 nH, DC Resistance 1 Ω → Quality Factor = 0.06283
- Inductor Peak Current Check Ipeak = Idc + V × Δt / (2 × L) Applied Voltage 0.33 V, On-Time 100 ns, Inductance 100 nH → Current Ripple = 0.33 A
- Mutual Inductance M = k × √(L1 × L2) Coupling Coefficient 2.5 %, Inductance 1 0.22 µH, Inductance 2 0.47 µH → Mutual Inductance = 8.039 nH
- Inductor DCR Power Loss P = I² × DCR Current 2 mA, DC Resistance 0.1 mΩ → Power Loss = 4 × 10⁻⁴ µW
- Toroid Core Inductance L = AL × N² AL Value 0.025, Number of Turns 0.055 → Inductance = 7.56 × 10⁻⁵ nH
- Core Loss (Steinmetz) Pv = K · f^x · B^y Steinmetz K 0.025, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118 → Core Loss Density = 0.01209 W/m³
- Inductor Temperature Rise ΔT = Ploss · Rth Total Loss 10 mW, Thermal Resistance 0.1 °C/W → Temperature Rise = 0.001 °C
- Inductor AC Winding Loss Pac = Iac² · Rac AC RMS Current 100 µA, AC Resistance 1 Ω → AC Loss = 0.01 µW
- Air-Coil Inductance (Wheeler) L = µ0·N²·π·r² / (l + 0.9·r) Number of Turns 0.025, Coil Radius 0.1 mm, Coil Length 0.22 mm → Inductance = 7.96 × 10⁻⁵ nH
Worked result for every Inductors formula
| Formula | Expression | Worked result |
|---|---|---|
| Inductive Reactance | XL = 2πfL | Frequency 100 Hz, Inductance 100 µH → Reactance = 62.83 mΩ |
| RL Time Constant | τ = L / R | Inductance 100 µH, Resistance 1 Ω → Time Constant = 100 µs |
| Inductor Energy | E = ½LI² | Inductance 100 µH, Current 2 mA → Energy = 2 × 10⁻⁴ µJ |
| Series Inductance | Ltotal = L1 + L2 + ... + Ln | Inductor Values 100 µH, 0.22 mH, 0.47 mH → Ltotal = 0.79 mH |
| Parallel Inductance | 1/Ltotal = 1/L1 + 1/L2 + ... + 1/Ln | Inductor Values 100 µH, 0.22 mH, 0.47 mH → 1/Ltotal = 6 × 10⁻⁵ |
| Inductor Quality Factor | Q = 2πfL / Rdc | Frequency 100 kHz, Inductance 100 nH, DC Resistance 1 Ω → Quality Factor = 0.06283 |
| Inductor Peak Current Check | Ipeak = Idc + V × Δt / (2 × L) | Applied Voltage 0.33 V, On-Time 100 ns, Inductance 100 nH → Current Ripple = 0.33 A |
| Mutual Inductance | M = k × √(L1 × L2) | Coupling Coefficient 2.5 %, Inductance 1 0.22 µH, Inductance 2 0.47 µH → Mutual Inductance = 8.039 nH |
| Inductor DCR Power Loss | P = I² × DCR | Current 2 mA, DC Resistance 0.1 mΩ → Power Loss = 4 × 10⁻⁴ µW |
| Toroid Core Inductance | L = AL × N² | AL Value 0.025, Number of Turns 0.055 → Inductance = 7.56 × 10⁻⁵ nH |
| Core Loss (Steinmetz) | Pv = K · f^x · B^y | Steinmetz K 0.025, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118 → Core Loss Density = 0.01209 W/m³ |
| Inductor Temperature Rise | ΔT = Ploss · Rth | Total Loss 10 mW, Thermal Resistance 0.1 °C/W → Temperature Rise = 0.001 °C |
| Inductor AC Winding Loss | Pac = Iac² · Rac | AC RMS Current 100 µA, AC Resistance 1 Ω → AC Loss = 0.01 µW |
| Air-Coil Inductance (Wheeler) | L = µ0·N²·π·r² / (l + 0.9·r) | Number of Turns 0.025, Coil Radius 0.1 mm, Coil Length 0.22 mm → Inductance = 7.96 × 10⁻⁵ nH |
Variables used across Inductors formulas
- XL — Inductive reactance in ohms (Ω)
- f — Frequency in hertz (Hz)
- L — Inductance in henries (H)
- τ — Time constant in seconds (s)
- R — Resistance in ohms (Ω)
- E — Energy in joules (J)
- I — Current through the inductor (A)
- Ltotal — Total equivalent inductance (H)
- L1, L2, ... Ln — Individual inductor values (H)
- Q — Quality factor (dimensionless)
- Rdc — DC winding resistance (Ω)
- ΔI — Peak-to-peak current ripple (A)
- V — Voltage across inductor during on-time (V)
- Δt — Switch on-time (s)
- M — Mutual inductance (H)
- k — Coupling coefficient (0 to 1, dimensionless)
- L₁ — Self-inductance of coil 1 (H)
- L₂ — Self-inductance of coil 2 (H)
- P — Power dissipated as heat (W)
- DCR — DC winding resistance (Ω)
- AL — Core inductance factor (nH/turn²)
- N — Number of turns (dimensionless)
- Pv — Core loss per unit volume (W/m³)
- K — Steinmetz coefficient (material constant)
- B — Peak AC flux density (T)
- x — Frequency exponent (≈1.1–1.7)
- y — Flux-density exponent (≈2–3)
- ΔT — Temperature rise above ambient (°C)
- Ploss — Total power dissipated (copper + core) (W)
- Rth — Thermal resistance to ambient (°C/W)
- Pac — AC winding loss (W)
- Iac — RMS ripple current at the switching frequency (A)
- Rac — AC resistance at that frequency (Ω)
- r — Coil radius (m)
- l — Coil length (m)
Questions people ask about Inductors
- How to calculate inductance with a 8mh and 4mh in series — Series Inductance
- Wheeler formula single layer air core coil inductance — Air-Coil Inductance (Wheeler)
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