PCB & Traces Formulas

PCB and trace formulas relate copper geometry to current capacity, resistance, and temperature rise. These calculators help you choose trace widths and via counts that carry current safely. They are essential for power routing and high-current board design.

PCB & Traces Formula Calculators

Worked result for every PCB & Traces formula

Formula Expression Worked result
Trace Current Capacity (IPC-2221) I = k × ΔT^0.44 × A^0.725 Constant k 0.025, Temperature Rise (°C) 2.5 °C, Cross-Section (mil²) 10 mil² → I = 0.1986 A
Trace Resistance R = ρ × L / A (copper) Length (cm) 0.1 cm, Area (cm²) 0.1 cm² → Resistance = 0.001724 mΩ
Trace Voltage Drop Vdrop = I × R Current 2 mA, Trace Resistance 1 Ω → Voltage Drop = 2 mV
Via Current Capacity (IPC-2221) I = k × ΔT^0.44 × A^0.725 Constant k 0.025, Temperature Rise (°C) 2.5 °C, Barrel Cross-Section (mil²) 10 mil² → I = 0.1986 A
Microstrip Impedance Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) Dielectric Constant εr 0.025, Dielectric Height (mm) 0.1 mm, Trace Width (mm) 0.22 mm, Copper Thickness (mm) 0.47 mm → Z₀ ≈ (87/√(εr+1.41)) × ln(5.98h/(0.8w+t)) = -5.607
Stripline Impedance Z0 = (60/√εr) × ln(4h/(0.67π×(0.8w+t))) Dielectric Constant εr 0.25, Dielectric Height (mm) 1 mm, Trace Width (mm) 0.47 mm, Copper Thickness (mm) 0.22 mm → Z0 = 139.1 Ω
Differential Pair Impedance Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) Single-Ended Z0 1 Ω, Trace Spacing (mm) 0.1 mm, Dielectric Height (mm) 0.22 mm → Zdiff ≈ 2 × Z0 × (1 − 0.48 × e^(−0.96s/h)) = 1.379
Near-End Crosstalk NEXT = Kb × length Coupling Factor (dB/m) 0.025 dB/m, Coupled Length 1 mm → Crosstalk (dB) = 2.5 × 10⁻⁵ dB
Via Inductance L = 5.08 × h × (ln(4h/d) + 1) nH Via Height (mm) 0.1 mm, Via Diameter (mm) 0.22 mm → L = 0.8117 nH
EMI Shielding Effectiveness SE = 20 × log10(Ei / Et) Incident Field 0.33 V, Transmitted Field 0.726 V → Shielding Effectiveness = -6.848 dB
Plane Spreading Resistance Rspread = ρ / (π × r) Resistivity (Ω·m) 0.025 Ω·m, Via/Pad Radius 0.1 mm → Spreading Resistance = 79.58 Ω
Transmission Line Propagation Delay td = length × √(LC) Trace Length 0.1 cm, Inductance per Unit Length 0.1 nH/cm, Capacitance per Unit Length 0.01 pF/cm → td = 1 × 10⁻¹³ s
Creepage/Clearance Estimate clearance ≈ Vpeak / 500 mm Peak Working Voltage 0.33 V → clearance ≈ Vpeak / 500 mm = 6.6 × 10⁻⁴
PCB Signal Propagation Velocity vp = c / √(εr_eff) Effective Dielectric Constant 0.055 → Propagation Velocity = 1.28 × 10⁹
Thermal Via Array Resistance Rarray = Rsingle / n Single Via Thermal R 0.22 °C/W, Number of Vias 0.025 → Array Thermal Resistance = 8.8 °C/W
Copper Weight to Thickness t = oz × 35 µm Copper Weight (oz/ft²) 0.025 → Copper Thickness = 8.75 × 10⁻⁴ mm
Annular Ring Width AR = (Dpad − Ddrill) / 2 Pad Diameter 0.47 mm, Drill Diameter 0.22 mm → Annular Ring = 0.125 mm
PCB Trace Signal Delay td = length / vp Trace Length 0.1 mm, Propagation Velocity 0.025 → Signal Delay = 4 ms
Controlled Impedance Tolerance ΔZ/Z = √((Δh/h)² + (Δw/w)² + (Δεr/εr)²) Δh/h (dielectric thickness) 2.5 %, Δw/w (trace width) 5.5 %, Δεr/εr (dielectric const.) 11.8 % → ΔZ/Z = 0.1326
Coplanar Waveguide Impedance Z0 = (30π/√εeff) · K(k′)/K(k) Signal Width 0.1 mm, Gap Width 0.22 mm, Dielectric Constant 0.025 → Impedance = 0.2568 kΩ
Signal Knee Frequency fknee = 0.5 / tr Rise Time 100 ps → Knee Frequency = 5 GHz
Transmission-Line Critical Length lcrit = tr / (2 · tpd) Rise Time 100 ps, Propagation Delay 0.1 ps/mm → Critical Length = 50 cm
Via Stub Resonant Frequency fres = c / (4 · lstub · √εr) Stub Length 0.1 mm, Dielectric Constant 0.025 → Resonant Frequency = 4740 GHz
Guided Wavelength in Dielectric λg = c / (f · √εr) Frequency 100 MHz, Dielectric Constant 0.025 → Guided Wavelength = 18.96 m

Variables used across PCB & Traces formulas

  • I — Maximum current (A)
  • k — Layer constant: 0.048 for external, 0.024 for internal traces
  • ΔT — Allowable temperature rise above ambient (°C)
  • A — Trace cross-sectional area (mil²)
  • R — Trace resistance (Ω)
  • ρ — Copper resistivity (1.724 × 10⁻⁶ Ω·cm)
  • L — Trace length (cm)
  • Vdrop — Voltage drop across the trace (V)
  • Z₀ — Characteristic impedance (Ω)
  • εr — Relative dielectric constant of substrate (FR-4 ≈ 4.2-4.8)
  • h — Height of dielectric between trace and ground plane (mm)
  • w — Trace width (mm)
  • t — Copper thickness (mm)
  • Z0 — Characteristic impedance (Ω)
  • Zdiff — Differential impedance (Ω)
  • s — Edge-to-edge spacing between traces (mm)
  • NEXT — Near-end crosstalk level (dB)
  • Kb — Backward coupling coefficient per unit length (dB/m)
  • length — Length of parallel (coupled) routing (m)
  • d — Via drill diameter (mm)
  • SE — Shielding effectiveness (dB)
  • Ei — Incident electric field strength (V/m)
  • Et — Transmitted electric field strength (V/m)
  • Rspread — Spreading resistance (Ω)
  • r — Radius of the current injection point (m)
  • td — Propagation delay (s)
  • L_per_unit — Inductance per unit length (H/m)
  • C_per_unit — Capacitance per unit length (F/m)
  • V_peak — Peak working voltage between conductors (V)
  • v_p — Propagation velocity (m/s)
  • ε_r_eff — Effective relative permittivity of the transmission line
  • R_array — Combined thermal resistance of the via array (°C/W)
  • R_single — Thermal resistance of one via (°C/W)
  • n — Number of vias in the array
  • oz — Copper weight in oz/ft²
  • AR — Annular ring width (m)
  • D_pad — Copper pad diameter (m)
  • D_drill — Finished drill hole diameter (m)
  • Δh/h — Relative tolerance of dielectric thickness (ratio)
  • Δw/w — Relative tolerance of trace width (ratio)
  • Δεr/εr — Relative tolerance of dielectric constant (ratio)
  • S — Centre signal-trace width (m)
  • W — Gap to each ground (m)
  • εeff — Effective permittivity ≈ (εr+1)/2
  • fknee — Knee frequency (Hz)
  • tr — Signal rise (or fall) time, 10–90% (s)
  • lcrit — Critical (electrically-long) length (m)
  • tpd — Propagation delay per unit length (s/m)
  • fres — Quarter-wave resonant frequency (Hz)
  • lstub — Length of the unused via stub (m)
  • c — Speed of light
  • λg — Guided wavelength in the medium (m)
  • f — Frequency (Hz)

Questions people ask about PCB & Traces

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