Interactive Resistor Color Code

Supports 4-band and 5-band resistors.

CLICK COLOR BAND TO CHANGE VALUE

4-Band 5-Band

1,000 Ω

±5% tolerance

📐 Calculation Method

How it works:
4-band: R = (D1 × 10 + D2) × 10^M ± T%
5-band: R = (D1 × 100 + D2 × 10 + D3) × 10^M ± T%
Where D = digit bands, M = multiplier, T = tolerance

Ceramic Capacitor Code Decoder

Enter 3-digit code (e.g., 104 = 10 + 4 zeros = 100,000 pF = 100 nF)

100 nF

📐 Calculation Method

Calculation:
Capacitance (pF) = XY × 10^Z
Where code = XYZ (e.g., 104 = 10 × 10^4 = 100,000 pF = 100 nF)

Ohm's Law Calculator

Enter any two values to solve for the others.

Voltage (V):

Current (A):

Resistance (Ω):

Power (W):

Enter any two values...

📐 Calculation Method

Formulas:
V = I × R (Voltage = Current × Resistance)
I = V / R (Current = Voltage / Resistance)
R = V / I (Resistance = Voltage / Current)
P = V × I = I² × R = V² / R (Power)

LED Resistor Calculator

Supply Voltage (V):

LED Forward Voltage (V):

Desired Current (mA):

100 Ω

¼W resistor recommended

📐 Calculation Method

Calculation:
R = (V_supply - V_forward) / I_LED
P = (V_supply - V_forward) × I_LED
Where V_forward = LED voltage drop, I_LED = desired current

RC Filter & Time Constant Calculator

Calculate cutoff frequency and time constant for low-pass filters.

Resistance (Ω):

Capacitance (F):

15.9 Hz

τ = 10 ms

📐 Calculation Method

Formulas:
f_cutoff = 1 / (2π × R × C)
τ (tau) = R × C (time constant)
At f_cutoff, signal is attenuated by -3dB (≈70.7%)

Battery Life Estimator

Estimate runtime for battery-powered projects.

Battery Capacity (mAh):

Average Current (mA):

40 hours

Assumes continuous operation

📐 Calculation Method

Calculation:
Runtime (hours) = Battery_Capacity (mAh) / Average_Current (mA)
Note: Actual runtime may be lower due to battery efficiency and discharge curves

UART Baud Rate Error Checker

Check error % for common microcontrollers.

MCU Clock (MHz):

Desired Baud:

0.00% error

Safe for communication

📐 Calculation Method

Calculation:
Divisor = Clock_Freq / (16 × Baud_Rate)
Actual_Baud = Clock_Freq / (16 × round(Divisor))
Error % = |Actual_Baud - Desired_Baud| / Desired_Baud × 100
Safe threshold: ≤ 2% error

Engineering Unit Converter

Real-time conversion between common electronics units.

Resistance: =

Capacitance: =

Current: =

📐 Calculation Method

Conversion factors:
Resistance: 1 MΩ = 1000 kΩ = 1,000,000 Ω
Capacitance: 1 µF = 1000 nF = 1,000,000 pF
Current: 1 A = 1000 mA = 1,000,000 µA

Universal Pinout Reference

GPIO, power, and peripheral mappings for common dev boards.

ESP32 (WROOM-32)

Pin	Function	Description
GPIO 21	I2C SDA	Data Line
GPIO 22	I2C SCL	Clock Line
GPIO 18/19	SPI MOSI/MISO	Serial Peripheral
GPIO 36 (VP)	ADC1_0	Analog Input
3V3	Power	3.3V Logic
GND	GND	Ground

Arduino Uno (R3)

Pin	Function	Description
A4	I2C SDA	Data
A5	I2C SCL	Clock
D0/D1	UART RX/TX	Serial
A0-A5	Analog	10-bit ADC
5V / 3.3V	Power	Voltage Rails

Raspberry Pi Pico (RP2040)

Pin	Function	Description
GP0/GP1	UART0 TX/RX	Serial
GP4/GP5	I2C0 SDA/SCL	I²C Bus 0
GP16-GP21	ADC	12-bit Analog
VSYS / 3V3	Power	System & Logic

STM32F103 (Blue Pill)

Pin	Function	Description
PA9/PA10	USART1 TX/RX	Serial
PB6/PB7	I2C1 SCL/SDA	I²C
PA0-PA7	ADC1	12-bit Inputs
3.3V	Power	Regulated

Teensy 4.0

Pin	Function	Description
18/19	I2C1 SDA/SCL	Fast I²C
0/1	Serial1 RX/TX	UART
A0-A9	ADC	10-bit, High Speed
3.3V	Power	500mA Capable

Comprehensive Hardware Troubleshooting

Board Not Powering On?

Check: (1) USB cable is data-capable, (2) correct voltage (3.3V vs 5V), (3) no short circuits, (4) EN/RESET pin not held low.

GPIO Not Responding?

Verify pin isn't used for boot mode (e.g., ESP32 GPIO 0, 2, 15). Some pins are input-only (e.g., ESP32 GPIO 34-39).

I²C Devices Not Detected?

Ensure pull-up resistors (4.7kΩ) on SDA/SCL. Check address with scanner. Confirm GND is shared between devices.

UART Garbage Output?

Mismatched baud rate or logic levels. Use 3.3V↔5V level shifter if needed. Check TX→RX wiring (not TX→TX!).

ADC Readings Unstable?

Add 100nF capacitor from analog input to GND. Avoid long wires. Ensure stable power supply (use LDO, not USB directly).

WiFi/BT Fails on ESP32?

Insufficient power! Use ≥500mA supply. Add 10–100µF capacitor near 3.3V pin. Avoid noisy switching regulators.

Resistor Value Wrong?

Gold/silver band is tolerance (right side). For 5-band, first 3 = digits. Double-check color under good light.

Capacitor Marked "104" but No Value?

It's 100nF! Ceramic caps use 3-digit code: first 2 = value, last = zeros (in pF). "104" = 10 + 0000 pF = 100,000 pF = 100nF.

LED Won't Light?

Check polarity (long leg = anode). Verify current-limiting resistor. Test with 3V coin cell directly (briefly!).

Motor/Relay Interfering with Logic?

Always use flyback diode across inductive load. Separate power supplies for logic and motor. Add ferrite beads.

RC Filter Not Working?

Ensure R and C values match desired cutoff. Use non-polarized caps for AC signals. Keep traces short to reduce parasitic capacitance.

Battery Drains Too Fast?

Measure sleep current. Disable unused peripherals. Use deep sleep modes. Consider higher capacity LiPo or 18650 cells.

Logic Level Voltage Matcher

Input Voltage (V):

3.33V

For 3.3V logic from 5V, use:
R1 = 10kΩ, R2 = 20kΩ (standard divider)

📐 Calculation Method

Voltage Divider Formula:
V_out = V_in × R2 / (R1 + R2)
For 5V → 3.3V: use R1=10kΩ, R2=20kΩ
V_out = 5V × 20kΩ / (10kΩ + 20kΩ) = 3.33V

Color Code ↔ Value Converter

Convert between resistor/capacitor values and color codes.

Enter Value (e.g., 4k7, 100n):

Brown, Black, Red, Gold

Supports: 4k7 = 4.7kΩ, 100n = 100nF, 2m2 = 2.2MΩ

📐 Calculation Method

Notation Guide:
4k7 = 4.7 kΩ (k for kilo)
2m2 = 2.2 MΩ (m for mega)
100n = 100 nF (n for nano)
22r = 22 Ω (r for decimal point)

I²C Pull-up Resistor Calculator

Calculate optimal pull-up resistors for I²C bus.

Bus Capacitance (pF):

Supply Voltage (V):

Bus Speed (kHz):

2.2 kΩ – 10 kΩ

Use 4.7kΩ for most cases

📐 Calculation Method

Calculation:
R_max = 300ns / (0.8473 × C_bus)
R_min = V_dd / 0.003A (3mA sink current)
Where C_bus = total bus capacitance (pF)
Typical range: 2.2kΩ – 10kΩ (4.7kΩ most common)

PCB Trace Width Calculator

Calculate minimum trace width per IPC-2221.

Current (A):

Copper Weight (oz):

Temp Rise (°C):

0.25 mm

≈ 10 mil (for 1 oz/ft² copper)

📐 Calculation Method

IPC-2221 Formula:
Area = [I / (k × ΔT^0.44)]^(1/0.725)
Width (mils) = Area / (thickness × 1.378)
Where k=0.048 (external), 0.024 (internal)
Thickness = oz/ft² (1 oz = 1.378 mils = 0.035mm)

ASCII ↔ Hex ↔ Binary Converter

Real-time conversion for serial debugging.

Hex: 48 65 6C 6C 6F

Binary: 01001000 01100101...

📐 Calculation Method

Conversion:
ASCII → Hex: char.charCodeAt(0).toString(16)
Hex → ASCII: String.fromCharCode(parseInt(hex, 16))
Decimal → Binary: dec.toString(2).padStart(8, '0')
Example: 'A' = 0x41 = 65 = 01000001

Pin Conflict Checker

Avoid boot-mode and restricted pins.

Select Board:

Enter Pin(s) (e.g., GPIO15, PA9):

Safe to use

📐 Calculation Method

Common Conflicts:
ESP32: GPIO0/2/15 (boot mode), GPIO12 (flash voltage)
STM32: PA11/12 (USB), PA13/14 (SWD debug)
RP2040: GP23/24 (power), GP25 (onboard LED)

💡 Power Calculator

Calculate power dissipation, energy consumption, and efficiency

Voltage (V):

Current (A):

Resistance (Ω):

Time (hours):

Power: 24 W

Energy: 24 Wh

📐 Power Formulas

Power Triangle:
P = V × I
P = V² / R
P = I² × R
Energy (Wh) = P × time (hours)
Energy (kWh) = P × time / 1000

⚡ Voltage Divider Calculator

Design precise voltage dividers with standard resistor values

Input Voltage (V_in):

Output Voltage (V_out):

Load Current (mA) [optional]:

R1 = 4.7 kΩ, R2 = 3.3 kΩ

Actual V_out: 4.95V, Power: 15.2mW

📐 Voltage Divider Formula

Basic Formula:
V_out = V_in × (R2 / (R1 + R2))

Design Rule:
Total current ≈ 10× load current for stable operation
R_total = R1 + R2 = V_in / I_divider

🔌 LM317 Voltage Regulator

Design LM317 adjustable regulator circuits

Desired Output Voltage (V):

R1 Value (Ω) [typically 240Ω]:

R2 = 1.2 kΩ

Actual V_out: 5.01V, I_adj: 50µA

📐 LM317 Formula

Output Voltage:
V_out = 1.25V × (1 + R2/R1) + I_adj × R2
V_ref = 1.25V (between OUT and ADJ)

Design Tips:
• R1: 240Ω typical (sets reference current)
• R2: varies for desired V_out
• V_in must be 3V above V_out minimum
• Add 0.1µF cap on ADJ for stability

LM317 Regulator Circuit — Example

Component Values:
R1 = 240Ω (standard)
R2 = 240Ω × (Vout/1.25V - 1)
Example: For 5V output:
R2 = 240Ω × (5/1.25 - 1) = 1.2kΩ
Input: Vin ≥ Vout + 3V (dropout)
Caps: C_in = 0.1µF, C_out = 1µF, C_adj = 10µF (optional for ripple reduction)

⚡ Zener Diode Regulator

Calculate series resistor for zener voltage regulation

Input Voltage (V):

Zener Voltage (V):

Load Current (mA):

Zener Current (mA) [5-10mA typical]:

R_s = 115 Ω

Power: 414mW (use ≥0.5W resistor)

📐 Zener Regulator Formula

Series Resistor:
R_s = (V_in - V_z) / (I_load + I_z)
P_R = (V_in - V_z) × (I_load + I_z)
P_zener = V_z × I_z

Design Tips:
• I_z = 5-10mA for stable regulation
• Add capacitor (100µF) for load transients
• Use next higher standard resistor value

🔄 Buck/Boost Converter Calculator

Design switching regulator inductors and duty cycles

Converter Type:

Input Voltage (V):

Output Voltage (V):

Output Current (A):

Switching Frequency (kHz):

Duty Cycle: 41.7%

L_min: 33µH, Efficiency: ~85%

📐 Converter Formulas

Buck Converter:
D = V_out / V_in
L_min = (V_in - V_out) × V_out / (ΔI × f × V_in)

Boost Converter:
D = 1 - (V_in / V_out)
L_min = V_in × D / (ΔI × f)

Buck-Boost:
D = V_out / (V_in + V_out)
ΔI = 20-40% of I_out (ripple current)

🔍 SMD Component Decoder

Decode SMD resistor and capacitor markings

Component Type:

SMD Code (e.g., 103, 4R7, 22):

10,000 Ω (10 kΩ)

3-digit code: 10 × 10³

📐 SMD Code Systems

Resistor Codes:
3-digit: XYZ → XY × 10^Z Ω
4-digit: WXYZ → WXY × 10^Z Ω
'R' notation: 4R7 = 4.7Ω, R47 = 0.47Ω

Capacitor Codes:
3-digit: XYZ → XY × 10^Z pF
Letter suffix: pF (A), nF (B), µF (C)
Example: 104 = 100,000pF = 100nF

🎯 E-Series Standard Value Finder

Find nearest standard resistor/capacitor values

Target Value:

E-Series:

Nearest: 4.7 kΩ

Error: 1.06% | Also available: 5.1 kΩ, 5.6 kΩ

📐 E-Series Standards

Standard Series:
E12: 12 values/decade (10%, 20%)
E24: 24 values/decade (5%)
E48: 48 values/decade (2%)
E96: 96 values/decade (1%)

Example E12:
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
(multiply by 10^n for other decades)

🔗 Series/Parallel Calculator

Calculate combined resistance and capacitance

Component Type:

Configuration:

Values (comma-separated, e.g., 10, 20, 30):

Total: 60 Ω

Series: R_total = R1 + R2 + R3

📐 Combination Formulas

Resistors & Inductors:
Series: R_T = R1 + R2 + R3 + ...
Parallel: 1/R_T = 1/R1 + 1/R2 + 1/R3 + ...

Capacitors (opposite!):
Series: 1/C_T = 1/C1 + 1/C2 + 1/C3 + ...
Parallel: C_T = C1 + C2 + C3 + ...

🎛️ RL Filter Calculator

Design inductive low-pass and high-pass filters

Filter Type:

Cutoff Frequency (Hz):

Resistance (Ω):

Inductance: 159 mH

Time constant τ = 159 µs

📐 RL Filter Formulas

Cutoff Frequency:
f_c = R / (2π × L)
L = R / (2π × f_c)

Time Constant:
τ = L / R

Impedance:
X_L = 2π × f × L (inductive reactance)

📻 RLC Resonant Circuit

Calculate resonance frequency and quality factor

Inductance (µH):

Capacitance (pF):

Resistance (Ω):

Resonance: 5.03 MHz

Q-Factor: 63.2, Bandwidth: 79.6 kHz

📐 RLC Resonance Formulas

Resonant Frequency:
f₀ = 1 / (2π × √(L × C))

Quality Factor:
Q = (1/R) × √(L/C) = X_L / R

Bandwidth:
BW = f₀ / Q

Impedance at Resonance:
Z = R (minimum for series, maximum for parallel)

📡 Wavelength Calculator

Calculate wavelength, frequency, and antenna dimensions

Frequency (MHz):

Velocity Factor (0.66-0.98):

Wavelength: 65.9 cm

λ/4: 16.5 cm, λ/2: 33.0 cm (antenna lengths)

📐 Wavelength Formulas

Wavelength:
λ = c / f = (3×10⁸ m/s) / f
λ_actual = λ × VF (velocity factor)

Antenna Dimensions:
Dipole: λ/2
Quarter-wave: λ/4
Full-wave: λ

Velocity Factors:
Free space: 1.0, Coax (RG-58): 0.66, Wire in air: 0.95

📊 VSWR & Return Loss

Calculate transmission line match quality

Mode:

Characteristic Impedance Z₀ (Ω):

Load Impedance Z_L (Ω):

VSWR or Return Loss (dB):

VSWR: 1.50:1

Return Loss: 14.0 dB, Reflection: 20%

📐 VSWR Formulas

VSWR (Voltage Standing Wave Ratio):
VSWR = (1 + |Γ|) / (1 - |Γ|)
Γ = (Z_L - Z₀) / (Z_L + Z₀) (reflection coefficient)

Return Loss:
RL = -20 × log₁₀(|Γ|) dB

Power Reflected:
P_refl = |Γ|² × 100%

💡 LED Array Calculator

Design series/parallel LED arrays with current limiting

Supply Voltage (V):

LED Forward Voltage (V):

LED Current (mA):

Number of LEDs:

Configuration: 3 LEDs × 2 strings

R = 150Ω per string, P = 120mW each

📐 LED Array Design

Series LEDs per string:
N_series = floor(V_supply / V_f)

Current Limiting Resistor:
R = (V_supply - N × V_f) / I_LED
P_R = (V_supply - N × V_f) × I_LED

Parallel Strings:
N_parallel = Total LEDs / N_series

⏱️ 555 Timer Calculator

Design astable and monostable 555 timer circuits

Mode:

Frequency/Time: Hz

Duty Cycle (%):

C (µF):

R1 = 1 kΩ, R2 = 6.8 kΩ

Actual f = 1.02 kHz, Duty = 53%

📐 555 Timer Formulas

Astable Mode:
f = 1.44 / ((R1 + 2×R2) × C)
Duty Cycle = (R1 + R2) / (R1 + 2×R2) × 100%
T_high = 0.693 × (R1 + R2) × C
T_low = 0.693 × R2 × C

Monostable Mode:
T_pulse = 1.1 × R × C

💎 Crystal Oscillator Calculator

Design crystal oscillator load capacitors

Crystal Frequency (MHz):

Load Capacitance C_L (pF):

Stray Capacitance C_stray (pF):

C1 = C2 = 22 pF

Actual C_L = 16 pF, Period = 62.5 ns

📐 Crystal Load Capacitor Formula

Load Capacitance:
C_L = (C1 × C2) / (C1 + C2) + C_stray

For equal caps (C1 = C2):
C1 = C2 = 2 × (C_L - C_stray)

Typical Values:
C_L: 12-22pF (check datasheet)
C_stray: 2-5pF (PCB + pin capacitance)

🔺 BJT Bias Calculator

Design voltage divider bias for BJT amplifiers

Supply Voltage V_CC (V):

Collector Current I_C (mA):

DC Gain (β / h_FE):

V_CE Operating Point (V):

R_C = 560Ω, R_E = 470Ω

R1 = 10kΩ, R2 = 2.2kΩ, V_B = 1.91V

📐 BJT Biasing Formulas

Voltage Divider Bias:
V_E = 0.1 × V_CC (rule of thumb)
V_B = V_E + 0.7V (silicon BJT)
R_E = V_E / I_E ≈ V_E / I_C
R_C = (V_CC - V_CE - V_E) / I_C

Base Resistors:
I_divider = 10 × I_B = 10 × I_C / β
R2 = V_B / I_divider
R1 = (V_CC - V_B) / I_divider

🎛️ MOSFET Gate Drive Calculator

Calculate gate resistor and switching times

Gate Charge Q_g (nC):

Gate-Source Capacitance C_iss (pF):

Drive Voltage V_drive (V):

Desired Switch Time (ns):

R_gate = 22 Ω

t_rise = 115 ns, Peak I_gate = 545 mA

📐 MOSFET Gate Drive Formulas

Gate Resistor:
R_gate = t_switch / (2.2 × C_iss)

Switching Time:
t_rise/fall ≈ 2.2 × R_gate × C_iss

Peak Gate Current:
I_gate(peak) = V_drive / R_gate

Power Dissipation:
P_sw = C_iss × V_drive² × f_sw

📈 Op-Amp Gain Calculator

Design inverting and non-inverting amplifier circuits

Configuration:

Desired Gain (V/V or dB):

Input Impedance (kΩ) [for inverting]:

R1 = 10 kΩ, R2 = 90 kΩ

Actual Gain = 10 V/V (20 dB), Input Z = 10 kΩ

📐 Op-Amp Gain Formulas

Non-Inverting:
A_v = 1 + (R2 / R1)
V_out = V_in × A_v

Inverting:
A_v = -(R2 / R1)
V_out = -V_in × (R2 / R1)
Z_in = R1

Differential:
V_out = (R2/R1) × (V2 - V1)

Inverting Amplifier — Example

Gain: A_v = -R2 / R1
Example: R1 = 10 kΩ, R2 = 100 kΩ → A_v = -10

Non-Inverting Amplifier — Example

Gain: A_v = 1 + (R2 / R1)
Example: R1 = 10 kΩ, R2 = 90 kΩ → A_v = 10

Differential Amplifier — Example

Gain: V_out = (R2 / R1) × (V2 - V1)
Example: R1 = 10 kΩ, R2 = 10 kΩ → unity differential gain

🔌 RS-485 Termination Calculator

Calculate termination resistors for RS-485 networks

Cable Characteristic Impedance (Ω):

Number of Nodes:

Cable Length (m):

Baud Rate (bps):

Termination: 120 Ω at both ends

Max length OK, Bias: 560Ω pullup, 560Ω pulldown

📐 RS-485 Design Rules

Termination Resistor:
R_term = Z₀ (cable impedance, typically 120Ω)
Place at both ends of the bus

Bias Resistors (optional):
R_pullup = R_pulldown ≈ 560Ω
Ensures defined idle state

Cable Length Limits:
115200 baud: ~1200m
1 Mbaud: ~100m
10 Mbaud: ~12m

⚡ KVL/KCL Circuit Solver

Solve simple series and parallel circuits using Kirchhoff's Laws

Circuit Type:

Source Voltage (V):

Resistances (Ω, comma-separated):

Total Current: 18.5 mA

R_total = 650Ω, Power: 222 mW

📐 Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL):
ΣV = 0 (sum of voltages in closed loop = 0)
V_source = V_R1 + V_R2 + V_R3 + ...

Kirchhoff's Current Law (KCL):
ΣI = 0 (sum of currents at node = 0)
I_in = I_out1 + I_out2 + I_out3 + ...

Series: Same current, voltages add
Parallel: Same voltage, currents add

⚖️ Wheatstone Bridge

Find an unknown resistance using a balanced bridge circuit. When balanced: R1/R2 = R3/R4

Mode:

R1 (Ω):

R2 (Ω):

R3 (Ω):

R4 (Ω):

Supply Voltage Vs (V):

Enter values above

Balance condition: R1/R2 = R3/R4

📐 Wheatstone Bridge Theory

Balanced Bridge:
R1/R2 = R3/R4 → V_out = 0V

Find Unknown R:
R4 = R2 × R3 / R1

Output Voltage (unbalanced):
V_out = Vs × (R4/(R3+R4) − R2/(R1+R2))

Common Uses:
• Strain gauges & load cells
• Temperature sensors (thermistors)
• Pressure sensors
• Precise resistance measurement

🌡️ Heatsink & Thermal Calculator

Calculate junction temperature and required heatsink thermal resistance

Power Dissipated (W):

Max Junction Temp Tj (°C):

Ambient Temp Ta (°C):

θjc — Junction to Case (°C/W):

θcs — Case to Heatsink (°C/W):

Enter values above

Tj = Ta + P × (θjc + θcs + θsa)

📐 Thermal Resistance Chain

Junction Temperature:
Tj = Ta + P × (θjc + θcs + θsa)

Required Heatsink θsa:
θsa = (Tj_max − Ta) / P − θjc − θcs

Typical Values:
θcs with thermal paste: 0.1–0.5 °C/W
θcs dry / mica pad: 0.5–1.5 °C/W
Free-air heatsink: 5–30 °C/W
Forced-air heatsink: 1–10 °C/W

🔥 Fuse Sizing Calculator

Select the correct fuse rating for a circuit

Load Current (A):

Safety Margin:

Fuse Type:

Enter load current

Next standard rating shown

📐 Standard Fuse Ratings

IEC Standard Ratings (A):
0.1, 0.16, 0.2, 0.25, 0.315, 0.4, 0.5, 0.63,
0.8, 1, 1.25, 1.6, 2, 2.5, 3.15, 4, 5, 6.3,
8, 10, 12.5, 16, 20, 25, 32, 40, 50, 63A

Rule of thumb:
Fuse rating = Load current × safety margin
Round UP to next standard value

Fast-blow: Signal/semiconductor protection
Slow-blow: Motors, transformers, PSUs
Anti-surge: General electronics

🔄 Transformer Calculator

Turns ratio, secondary voltage/current, and efficiency

Mode:

Primary Voltage Vp (V):

Secondary Voltage Vs (V):

Primary Turns Np:

Primary Current Ip (A):

Efficiency (%):

Enter values above

Np/Ns = Vp/Vs = Is/Ip

📐 Transformer Formulas

Turns Ratio: n = Np/Ns = Vp/Vs

Secondary Voltage: Vs = Vp × Ns/Np

Secondary Current: Is = Ip × Np/Ns × η

Output Power: Pout = Vs × Is

Efficiency: η = Pout / Pin × 100%

Note: After rectification, DC voltage
≈ Vs(rms) × 1.414 − 1.4V (bridge losses)

⚡ Capacitor Energy & Charge

Energy stored, charge time, and discharge calculations

Capacitance (µF):

Voltage (V):

Series Resistance for RC (Ω):

Enter values above

E = ½CV²

📐 Capacitor Formulas

Energy Stored: E = ½ × C × V² (Joules)

Charge Stored: Q = C × V (Coulombs)

RC Time Constant: τ = R × C
63.2% charged at 1τ, 99.3% at 5τ

Charge Time (to % of V):
t = −τ × ln(1 − V_target/V_supply)

Capacitive Reactance:
Xc = 1 / (2π × f × C)

⚡ Inrush Current & NTC Sizing

Calculate inrush current and select NTC thermistor limiter

Supply Voltage (V):

Filter Capacitance (µF):

Circuit Resistance (Ω):

Steady-State Current (A):

Enter values above

I_inrush = Vpeak / R_total

📐 Inrush Theory

Peak Inrush: I_peak = V_peak / R_series
V_peak = V_rms × √2 ≈ V_rms × 1.414

NTC Thermistor Sizing:
R_ntc_cold = V_peak / I_max_allowed
Choose NTC with R25 ≥ this value
Steady-state loss = I²ss × R_ntc_hot

Rule of thumb:
Inrush can be 20–100× steady-state current
NTC reduces this to 3–10× safely

Alternatives: Series resistor + relay bypass,
active inrush controller ICs (e.g. TPS2490)

📉 Component Derating Calculator

Calculate safe operating limits with temperature derating

Component Type:

Rated Max Value:

Operating Temp (°C):

Derating Policy:

Enter values above

Derated value = rated × derating factor

📐 Derating Guidelines

Resistors:
Full power to 70°C, derate to 0W at 155°C
P_safe = P_rated × (155 − T_op) / (155 − 70)

Capacitors:
Voltage derate 50–80% of rated voltage
Electrolytic: never exceed 80% V_rated
Ceramic: 50% for long-term reliability

Semiconductors:
Current derate linearly above 25°C
I_safe = I_rated × (Tj_max − T_op) / (Tj_max − 25)

🔌 Wire Gauge Calculator (AWG ↔ mm²)

Convert between AWG and metric, find current capacity and resistance

Input Mode:

AWG Size:

Cross-section (mm²):

Required Current (A):

Installation Type:

Select gauge above

Based on 60°C conductor temperature

📐 Quick AWG Reference

Diameter (mm): d = 0.127 × 92^((36−AWG)/39)

Area (mm²): A = π/4 × d²

Resistance (Ω/km, copper):
R = ρ / A = 0.01724 / A(mm²) × 1000

Common cable sizes (IEC):
0.5 mm² — signalling, 3A
1.0 mm² — lighting, 10A
1.5 mm² — ring mains, 16A
2.5 mm² — sockets, 20A
4.0 mm² — cooker/shower, 25A
6.0 mm² — sub-mains, 32A
10 mm² — supply tails, 43A

📉 Cable Voltage Drop Calculator

Calculate voltage drop over a cable run

Cable Length (m, one way):

Current (A):

Cable Cross-section (mm²):

Supply Voltage (V):

Conductor Material:

Enter values above

Vdrop = 2 × I × R (return path included)

📐 Voltage Drop Limits

Formula:
R_cable = ρ × (2L) / A
V_drop = I × R_cable

Acceptable Limits:
Mains wiring (IEC 60364): ≤ 3% (lighting), ≤ 5% (power)
12V automotive: ≤ 3% (≤ 0.36V)
24V systems: ≤ 3% (≤ 0.72V)
Low-voltage signal: ≤ 1%

Rule of thumb:
Double cable length = double voltage drop
Double cable area = half voltage drop

📊 dB Converter

Convert between dB, voltage ratio, and power ratio

Input Type:

Value (dB):

Enter value above

dB = 20·log₁₀(V₂/V₁) or 10·log₁₀(P₂/P₁)

📐 Common dB Values

Voltage: dB = 20 × log₁₀(Vout/Vin)
Power: dB = 10 × log₁₀(Pout/Pin)

Key values to memorise:
+3 dB = ×2 power, ×1.414 voltage
+6 dB = ×4 power, ×2 voltage
+10 dB = ×10 power, ×3.16 voltage
+20 dB = ×100 power, ×10 voltage
−3 dB = ½ power (−3dB point = cutoff freq)
−6 dB = ¼ power, ½ voltage
−20 dB = 1/100 power, 1/10 voltage

dBm: power relative to 1mW
0 dBm = 1mW, +30 dBm = 1W

🔢 ADC / DAC Resolution Calculator

LSB voltage, full-scale range, quantisation noise, and SNR

Resolution (bits):

Reference / Full-Scale Voltage (V):

Mode:

Select bits and Vref

LSB = Vref / 2^N

📐 ADC / DAC Formulas

LSB (Least Significant Bit):
LSB = Vref / 2^N

Theoretical SNR:
SNR = 6.02 × N + 1.76 dB

Digital code to voltage:
V = code × Vref / (2^N − 1)

Effective Number of Bits (ENOB):
ENOB = (SINAD − 1.76) / 6.02

Common Vref sources:
3.3V MCU supply, 5V supply,
2.048V / 2.5V / 4.096V precision ref ICs

🌊 PWM → Average Voltage Calculator

Calculate average voltage, RC filter values, and ripple

PWM Supply Voltage (V):

Duty Cycle (%):

PWM Frequency (Hz):

Filter Capacitor (µF):

Filter Resistor (Ω):

Enter values above

Vavg = Vsupply × Duty%

📐 PWM Filter Design

Average Voltage:
Vavg = Vsupply × (duty / 100)

RC Low-Pass Filter:
fc = 1 / (2π × R × C)
For good filtering: fc < PWM freq / 10

Ripple Voltage (approx):
Vripple ≈ Vavg / (f × R × C)

Use case examples:
LED dimming, motor speed control,
DAC replacement (with RC filter),
servo control (50Hz, 1–2ms pulse)

〰️ Schmitt Trigger / Comparator Hysteresis

Design hysteresis window for noise-immune threshold detection

Op-Amp Supply V+ (V):

Desired Trip Point (V):

Desired Hysteresis Width (V):

R1 (to reference/ground, Ω):

Enter values above

Vhyst = Vcc × R1 / (R1 + R2)

📐 Schmitt Trigger Formulas

Non-inverting Schmitt (positive feedback):
V_upper = Vcc × R1 / (R1 + R2)
V_lower = 0 × R1 / (R1 + R2) = 0 (rail-to-rail)

Hysteresis:
Vhyst = V_upper − V_lower
R2 = R1 × (Vcc − Vhyst) / Vhyst

Use when:
• Noisy signal crosses threshold
• Slow-moving signals (thermistors, LDRs)
• Converting sine waves to square waves
• Debouncing mechanical switches

🔐 CRC Calculator

Calculate CRC checksums for data verification

Input Data (hex bytes, space-separated):

CRC Algorithm:

Also compute:

Enter hex data above

Paste hex bytes from your protocol analyser

📐 CRC Reference

CRC-8: Simple, 1-byte, embedded sensors
CRC-8/MAXIM: Dallas 1-Wire, DS18B20
CRC-16: USB, Bluetooth
CRC-16/CCITT: SD cards, Xmodem
CRC-16/MODBUS: RS-485 Modbus RTU
CRC-32: Ethernet, ZIP, PNG files

Input format:
Hex pairs separated by spaces:
01 A2 FF 3C → 4 bytes

Use case:
Verify your microcontroller CRC matches
protocol spec before deploying to production