Online Tools
Everyday Electronics / Electrical / Mechanics / Thermodynamics / Electromagnetism Calculators
121 high-frequency electronics / electrical / mechanics / thermodynamics / electromagnetism calculators with SVG diagrams — enter parameters and get results instantly: resistor divider, DC-DC feedback resistors, TL431 feedback (flyback / forward), PCB impedance / current, motor sizing, power sizing, transformer, voltage drop, Coulomb’s law, Lorentz force, Faraday’s law, Carnot efficiency…
Resistor Voltage Divider
上臂 R1 接Input、下臂 R2 接地：既可按给定 R1/R2 算Output voltage，也可由Input量程and ADC 参数枚举标称Resistance，给出Source impedance合适的采样最佳组合。
Vout = Vin × R2 / (R1 + R2) ｜ ADC: R2/(R1+R2) = Vref(1−裕量)/Vin,maxSeries / Parallel Resistance
Equivalent resistance of series or parallel resistors, with k / M suffixes (e.g. 4.7k, 1M), up to 8 values.
series Rs = ΣRi ｜ parallel 1/Rp = Σ(1/Ri)Resistor Color Code
Read resistance and tolerance from 4- or 5-band codes; the bands render live in the diagram.
R = (significant digits) × multiplier ｜ 5-band adds one digitRC Filter / Cutoff Frequency
一阶 RC 低通 / 高通滤波Calculate：由 R、C 求Cutoff frequency fc and任意频点衰减，或由 fc 反推 R / C，或按 fc 推荐标准 R、C 组合。
fc = 1 / (2πRC) ｜ τ = RC ｜ R = 1/(2π·fc·C) ｜ C = 1/(2π·fc·R)LC Resonance Frequency
LC 回路的谐振Frequencyand特性阻抗：由 L、C 求 f0，或由 f0 反推 L / C，或按 f0 推荐标准 L、C 组合，用于选频网络、days线匹配andsupply滤波。
f0 = 1 / (2π√(LC)) ｜ Z0 = √(L/C) ｜ L = 1/((2π·f0)²·C) ｜ C = 1/((2π·f0)²·L)SMD Resistor Marking Calculator
Convert SMD resistor markings and resistance in both directions: 3-digit code (103 = 10 kΩ), 4-digit code (1002 = 10 kΩ), R decimal notation (4R7 = 4.7 Ω, R47 = 0.47 Ω) and EIA-96 precision code (01C = 10 kΩ), including all-zero jumpers.
3-digit AB×10^C | 4-digit ABC×10^D | R as decimal point | EIA-96: index (01–96) × multiplier letterDC-DC Feedback Resistor Selection
From Vref and target output voltage, enumerate the best divider across E3–E192 series and report actual error.
Vout = Vref × (1 + R1/R2)LED Current-Limiting Resistor
Current-limiting resistor, dissipation, and recommended package power from supply, LED forward voltage, and current.
R = (Vin − Vf) / IfOhm’s Law / Power
From any two quantities (U/I/R/P), solve the other two — the universal starting point for circuit checks.
U = IR ｜ P = UI = I²R = U²/RLDO Dropout Dissipation / Junction Temperature
Linear regulator dissipation, junction temperature, and efficiency — check thermals before selecting parts when dropout is large.
P = (Vin − Vout) × Iout ｜ Tj = Ta + P × θJABattery Life Estimate
Estimate runtime from capacity, average current, and usable depth of discharge, plus battery energy in Wh.
runtime = capacity × usable ratio / average currentSense-Resistor Current Measurement
Voltage drop, amplified output, and dissipation of a low-side sense resistor, with an ADC range check.
Vsh = I × Rsh ｜ Vout = Vsh × GPower Supply Sizing (Load Profile)
Determine rated supply tier, input power, and buffer capacitor from steady/peak current and load profile (resistive / capacitive / inductive / pulse).
P = max(U·I_pk, U·I_load·(1+margin)) ｜ I_in = P/(η·U_in·cosφ) ｜ C ≥ ΔI·t_pk/ΔVTL431 Shunt Regulator / Output Setting
The most common TL431 circuit: R1/R2 divider sets the output (optimal combination enumerated across E3–E192), plus the series resistor Rs, resistor and TL431 dissipation, and cathode-current checks.
Vout = Vref × (1 + R1/R2) ｜ Rs = (Vin − Vout)/(Iload + Ika_min + I_sense)TL431 + optocoupler Flybackfeedback calculation
Typical secondary-side TL431+optocoupler feedback for flyback: enumerate the divider from standard series, compute the LED limiting resistor, and derive the required primary current with CTR margin checks.
Vout = Vref × (1 + Ru/Rl) ｜ R_led = (Vled − Vf − Vka)/If ｜ If_min = Ic / CTR_minTL431 + optocoupler Forwardfeedback calculation
Typical secondary-side TL431+optocoupler feedback for forward: divider, LED limiting resistor, primary-side current derivation and margin checks (tap after the output LC filter; see notes for compensation).
Vout = Vref × (1 + Ru/Rl) ｜ R_led = (Vled − Vf − Vka)/If ｜ If_min = Ic / CTR_minPCB Trace Current Capacity
Safe current from width, copper weight, and allowed temperature rise per IPC-2221, plus trace resistance / drop.
I = k · ΔT^0.44 · A^0.725 (A in mil²)PCB Trace Width for Current
Work backwards per IPC-2221: from current and allowed rise, find minimum width rounded to 0.1mm.
A = (I/k)^(1/0.725) ｜ W = A / TPCB Characteristic Impedance
Quick characteristic impedance for microstrip / symmetric stripline (IPC-2141); check before routing USB, Ethernet, or RF traces.
microstrip Z0 = 87/√(εr+1.41) · ln[5.98h/(0.8w+t)]PCB Trace Resistance
DC resistance, drop, and dissipation from length, width, and copper weight — essential for long supply / sense traces.
R = ρ · L / (W · T), ρcopper = 1.724e-8 Ω·mVia current / resistance
Via resistance and current capacity from drill, board thickness, and plating — check before switching layers at high current.
R = ρ·L/A ｜ A = π/4·[(d+2t)² − d²]PCB Differential Pair Impedance
Edge-coupled differential impedance from width, spacing, and dielectric thickness; compare to 90/100/120Ω targets with tuning hints.
Zdiff = 2·Z0·(1 − k·e^(−c·s/h))｜microstrip k=0.48 c=0.96, stripline k=0.34 c=2.9PCB Spiral Inductor Designer
Planar spiral coil: inductance, DC resistance, rough Q, self-resonance, and current from turns, width, spacing, and outer diameter.
L = K1·µ0·n²·d_avg/(1+K2·ρ)｜d_in = d_out − 2n·w − (2n−1)·sPCB Planar Transformer Designer
Planar transformer design: turns from the volt-second equation, rounded ratio, flux check, winding width/layers, and copper loss.
N1 ≥ Vin·D/(k_vs·f·B·Ae)｜n = N2/N1 = Vout/(k_v·Vin·D)NFC PCB Antenna Design
13.56MHz PCB NFC antenna: square spiral inductance, resonance tuning capacitor (E6), Q and damping resistor, and read-range estimate.
L modified Wheeler｜C = 1/((2πf)²·L) − Cp｜H(d) = n·I·a²/(2(a²+d²)^1.5)WiFi/BT PCB Antenna Design
2.4GHz PCB antenna: λ/4 inverted-F (IFA) arm length or half-wave patch W/L/feed inset, with 50Ω feed width and clearance notes.
λ/4 arm = c/(4f·√εeff)｜patch W = c/(2f)·√(2/(εr+1)), L = c/(2f·√εeff) − 2ΔL555 Timer Frequency
Frequency / pulse width / duty for astable (square-wave) and monostable (fixed pulse) configurations.
astable f = 1.44/[(R1+2R2)C] ｜ monostable T = 1.1·R·CADC Code ↔ Voltage
Convert between ADC raw code and voltage, with 1 LSB resolution — handy for sensor calibration and serial raw data.
V = code / 2ⁿ × Vref ｜ 1 LSB = Vref / 2ⁿPWM Resolution / Counts
Achievable bits and duty step from timer clock and PWM frequency, or verify a target resolution.
counts = Fclk / Fpwm ｜ bits = log₂(counts)UART Baud Rate Divider
Baud divider and actual error from the peripheral clock (16× / 8× oversampling); large error means unreliable comms.
div = Fclk / (OS × baud) ｜ error ≤ ±2% recommendedAC Power / Power Factor
Active / reactive / apparent power from voltage, current and power factor, auto-switching single/three phase.
P = UI·cosφ ｜ 3-phase S = √3·U·I ｜ Q = S·sinφMotor Rated Current
Rated current from power, efficiency, and power factor, with the "≈2A per kW at 380V 3-phase" rule-of-thumb check.
I = P / (√3·U·η·cosφ) (three-phase)Transformer Ratio / Turns
Turns ratio from primary/secondary voltage; enter either side’s turns to derive the other.
U1/U2 = N1/N2 = kTransformer Capacity ↔ Rated Current
Primary/secondary rated current from kVA and voltage level — for breaker selection and protection settings.
I = S / (√3·U) (3-phase) ｜ single-phase I = S / UVoltage Drop / Wire Size Check
Voltage drop percentage from conductor material and cross-section, and the minimum section for an allowed drop — essential for long runs.
ΔU = 2·I·L·ρ/S (single-phase) ｜ √3·I·L·ρ/S (three-phase)Wire Cross-Section (Current)
Estimate cross-section from load current and rule-of-thumb current density, rounded to standard sizes.
S = I / J (J: copper open 6 / conduit 5 A/mm²; aluminum one tier lower)Reactance (XL / XC)
Inductive and capacitive reactance at line (or any) frequency, to guide compensation and filtering.
XL = 2πfL ｜ XC = 1/(2πfC)Reactive Power Compensation
Required kvar from current to target power factor — the cure for power-factor penalties.
Qc = P · (tanφ1 − tanφ2)Energy / Electricity Cost
Energy and cost from power and runtime; compare before/after efficiency upgrades at a glance.
W = P · t (kWh) ｜ cost = W × rateStar ↔ Delta Resistor Conversion
Simplify balanced three-phase networks: Y↔Δ resistor conversion for unbalanced networks.
Y→Δ: RΔ = R1+R2+R1R2/R3 ｜ Δ→Y: RY = adjacent product/ΣRMotor Sizing (Load Torque)
Size AC induction, DC, or brushed/brushless motors by load profile (constant torque / power / quadratic / shock): power, standard tier rounding, torque and overload check.
P_L = T_L·n_L/9550 ｜ P_N ≥ K·P_L/η_t ｜ T_N = 9550·P_N/n_N ｜ peak ≤ λ·T_NBuck step-down design
Enter design targets (voltage range / temperature rise / ripple / mode / frequency) to get the inductor, input/output capacitors, MOS SOA, gate resistor, and thermal design in one go.
D = Vout/Vin ｜ L = (Vin−Vout)·D/(ΔIL·fsw)Boost step-up design
Enter design targets to get the inductor (with RHP-zero check band), input/output capacitors, MOS SOA, gate resistor, and thermal design.
D = 1−Vin/Vout ｜ L = Vin·D/(ΔIL·fsw)Buck-Boost step-up/down design
Enter design targets (output taken as absolute value, polarity inverted) to get the inductor, input/output capacitors, MOS SOA, gate resistor, and thermal design.
D = |Vout|/(Vin+|Vout|) ｜ L = Vin·D/(ΔIL·fsw)RC Snubber Design
Ring damping for MOS / relay switching nodes: dual-frequency extraction of strays, with R/C values, loss, and an impedance Bode plot.
f_ring = 1/(2π√(LC)) ｜ R = √(L/C) ｜ Cs = 2~3Cp ｜ P = Cs·ΔV²·fswRCD / RDC Clamp Snubber Design
RCD clamp for flyback leakage spikes: clamp resistor / capacitor / ultrafast diode values, loss, and drain stress.
R = 2Vc(Vc−Vro)/(Llk·Ipk²·fsw) ｜ C = Vc/(R·ΔV·fsw) ｜ P = ½Llk·Ipk²·fsw·Vc/(Vc−Vro)Modbus RTU Frame & CRC16
Pack/unpack Modbus RTU frames (master request / slave response), compute the CRC-16/MODBUS checksum, and decode frames — matched against the standard frame format.
Frame = Slave + Function + Data + CRC16 (low byte first) | CRC-16/MODBUS init 0xFFFFModbus TCP Frame & MBAP
Pack/unpack Modbus TCP frames (master request / slave response) with MBAP header decoding, protocol-ID and length self-checks — matched against the standard frame format.
Frame = MBAP (Transaction ID + Protocol ID + Length + Unit ID) + Function + DataFrequency–Wavelength Calculator
Frequency ↔ wavelength conversion: vacuum/medium wavelength, period, velocity factor, half/quarter-wave antenna sizes, and photon energy.
λ = c / f | in medium λ′ = c / (f·√εr) | T = 1 / fRipple Filter Capacitor Calculator
Compute the required filter capacitance from ripple current, ripple frequency and allowed ripple: mains rectifier (full/half-wave), buck output triangular ripple, and sinusoidal ripple.
C = I / (K·f·ΔV) | full-wave K=2 · half-wave K=1 · buck K=8 · sine K=2πDecibel (dB) Calculator
Convert ratios, power and voltage to and from decibels: power ratio ↔ dB, voltage ratio ↔ dB, absolute power (dBm / dBW), voltage level (dBV / dBu / dBμV) and cascaded gain.
dB = 10·log10(P2/P1) = 20·log10(V2/V1) | dBm = 10·log10(P/1mW)Celsius ↔ Fahrenheit Temperature Converter
Convert between Celsius (°C), Fahrenheit (°F), Kelvin (K) and Rankine (°R): enter any one scale to get the other three, with an absolute-zero check.
°F = °C × 9/5 + 32 | K = °C + 273.15 | °R = K × 9/5Hysteresis Comparator (Schmitt Trigger)
Comparator positive-feedback hysteresis network: for the inverting / non-inverting topologies, derive the upper and lower trip points and hysteresis width from R1/R2 and the output swing, bound the width / trip-point error with the resistor tolerance, or pick standard resistors and a reference voltage from target trip points.
ΔV = (Voh − Vol)·R1/(R1+R2) (inverting) | ΔV = (Voh − Vol)·R1/R2 (non-inverting)Non-inverting op-amp calculator
Non-inverting op-amp stage: derive the voltage gain from Rf/Rg, or pick standard resistors for a target gain, then use the resistor tolerance to bound the gain error, and check gain-bandwidth and slew-rate limits (closed-loop bandwidth, full-power bandwidth, rise time).
A = 1 + Rf/Rg | BW = GBW / A | SR = 2π·f·Vpk | FPBW = SR / (2π·Vpk) | A_range = 1 + Rf(1±t)/Rg(1∓t)Differential op-amp calculator
Four-resistor difference (subtractor) amplifier: compute the output, differential gain, common-mode gain and CMRR from R1–R4 and two inputs, bound the gain / output error and worst-case CMRR with the resistor tolerance, or match standard resistors to a target gain, and check input impedance, bandwidth and slew rate.
Vout = V2·R4/(R3+R4)·(1+R2/R1) − V1·R2/R1 | when matched, Vout = Ad·(V2−V1), Ad = R2/R1Inverting op-amp calculator
Inverting op-amp stage: derive the voltage gain (A = −Rf/Rin) and input impedance from Rf/Rin, or pick standard resistors for a target gain, then use the resistor tolerance to bound the gain / output error and maximum mismatch error, and check noise-gain bandwidth and slew rate.
A = −Rf/Rin (|A| = Rf/Rin) | Zin = Rin | BW = GBW/(1+|A|) | SR = 2π·f·Vpk | FPBW = SR/(2π·Vpk)BPF op-amp band-pass filter designer (single-op-amp Sallen-Key)
Single-op-amp Sallen-Key band-pass filter (BPF) designer: given the high-pass / low-pass corner frequencies (fL, fH) or the center frequency and bandwidth (f0, BW), it automatically picks C1 and R4 and derives every R/C value, with standard-value rounding plus slew-rate and GBW checks and a Bode plot.
Auto C1 (so R1 ≈ 33 kΩ) | k = 2π·f0·C1 | H = (6.5 − 1/Q)/3 | C2 = C1/2 | R1 = 2/k, R2 = 2/(3k), R3 = 4/k, R5 = R4/(H−1) (auto R4 so R5 ≈ 10 kΩ) | Q = f0/BWOp-amp voltage-controlled resistor (VCR) designer
Single-op-amp voltage-controlled resistor (VCR) designer: a JFET (or a MOSFET in its ohmic region) acts as the variable resistor R_DS in the feedback path of an inverting amplifier, with an AN105 linearization network (equal R_L1/R_L2 across D-G and S-G) that decouples R_DS from the signal level and keeps the pass device in its ohmic region. Compute the equivalent resistance and voltage-controlled gain from the control voltage, or Vc from a target resistance, with linear-swing, sensitivity and bandwidth checks.
JFET: R_DS = V_P² / [2·I_DSS·(V_GS − V_P)] ｜ MOSFET: R_DS = 1 / [k·(V_GS − V_TH)] ｜ V_GS = Vc − V_S ≈ Vc (virtual-ground source) ｜ A = −R_DS / Rg ｜ |V_DS| < V_GS − V_th (R_L1 = R_L2 linearization)Impedance matching calculator (L / π / T)
Online design of L, π and T matching networks for RF and antennas: enter the source impedance Rs+jXs and load impedance RL+jXL to get the network Q, inductor and capacitor values, the approximate −3 dB bandwidth, and a circuit diagram of the chosen topology. Complex source / load reactances are compensated.
L: Q = √(Rhigh/Rlow − 1), Xseries = Q·Rlow, Bshunt = Q/Rhigh ｜ π: Rv = Rhigh/(Q²+1), Xseries = Rv(Q1+Q2) ｜ T: Rv = Rlow(Q²+1), Xseries = Q·R ｜ elements: L = X/ω, C = 1/(ωX)Unit Converter
Convert between units of length, area, volume, mass, pressure, force, energy, power, speed, time and temperature, plus common electrical quantities such as voltage, current, resistance, capacitance, inductance, frequency and charge: pick the from and to units to get the result, with a full comparison of every unit in the same quantity.
target = source × k_from ÷ k_to | temperature: °F = °C × 9/5 + 32Newton's Second Law Calculator (F=ma)
Compute the net force via F = m·a: enter mass and acceleration to get the force, with the weight W = m·g shown for reference.
F = m·a ｜ Weight W = m·g (g = 9.80665 m/s²)Pressure Calculator (P=F/A)
Compute pressure via P = F/A: enter the force and contact area to get results in Pa, kPa and MPa.
P = F / ATorque Calculator (τ=F·r·sinθ)
Compute the moment about an axis via τ = F·r·sinθ: enter force, lever arm and angle to get N·m and the effective lever arm.
τ = F·r·sinθWork Calculator (W=F·d·cosθ)
Compute work via W = F·d·cosθ: enter force, displacement and angle to get joules and kWh.
W = F·d·cosθMechanical Power Calculator (P=F·v)
Compute the instantaneous power of a traction force at constant velocity via P = F·v: enter force and speed to get W, kW and horsepower.
P = F·vKinetic Energy Calculator (Ek=½mv²)
Compute kinetic energy via Ek = ½mv²: enter mass and velocity to get joules and the equivalent drop height.
Ek = ½·m·v²Gravitational Potential Energy Calculator (Ep=mgh)
Compute gravitational potential energy via Ep = mgh: enter mass and height to get joules and the landing velocity.
Ep = m·g·hMomentum Calculator (p=mv)
Compute momentum via p = m·v: enter mass and velocity to get kg·m/s, with kinetic energy and equivalent impulse for reference.
p = m·vImpulse Calculator (J=F·Δt)
Compute impulse via J = F·Δt: enter force and duration to get N·s and the resulting momentum change.
J = F·ΔtSpring Force Calculator (Hooke's Law F=kx)
Compute spring force via Hooke's law F = k·x: enter stiffness and deformation to get the force and stored energy.
F = k·xElastic Potential Energy Calculator (Ep=½kx²)
Compute elastic potential energy via Ep = ½kx²: enter stiffness and deformation to get joules and the maximum release velocity.
Ep = ½·k·x²Spring-Mass Oscillator Period Calculator (T=2π√(m/k))
Compute the simple harmonic period via T = 2π√(m/k): enter mass and stiffness to get period, frequency and angular frequency.
T = 2π·√(m/k)Pendulum Period Calculator (T=2π√(L/g))
Compute the pendulum period via T = 2π√(L/g): enter length and gravity to get period and frequency (small-angle approximation).
T = 2π·√(L/g)Centripetal Force Calculator (F=mv²/r)
Compute the centripetal force via F = mv²/r: enter mass, velocity and radius to get the force and centripetal acceleration.
F = m·v²/r = m·ω²·rLinear & Angular Velocity Calculator (v=ωr)
Compute linear velocity via v = ω·r = 2πn·r/60: enter rotational speed and radius to get linear and angular velocity.
v = ω·r = 2π·n·r/60Torque-RPM-Power Calculator (P=τ·n/9549)
Convert motor torque, speed and power via P(kW) = τ(N·m)·n(rpm)/9549: pick any two known values to solve the third.
P = τ·n/9549 (P: kW · τ: N·m · n: rpm)Gear Ratio Calculator (i=z₂/z₁)
Compute the gear ratio via i = z₂/z₁: enter driving/driven tooth counts and input speed to get ratio, output speed and torque multiplication.
i = z₂/z₁ = n₁/n₂ = τ₂/τ₁Density Calculator (ρ=m/V)
Compute density via ρ = m/V: enter mass and volume (multiple units) to get kg/m³ and g/cm³, compared against water.
ρ = m / VFriction Force Calculator (f=μN)
Compute friction via f = μ·N: enter the coefficient and normal force (from direct input, mass or an incline) to get static/kinetic friction.
f = μ·NBuoyancy Calculator (Archimedes F=ρgV)
Compute buoyancy via Archimedes' principle F = ρ·g·V: enter liquid density and displaced volume.
F = ρ·g·VIdeal Gas Law Calculator (PV=nRT)
Solve any one of pressure, volume, amount of substance or temperature from the ideal gas law PV = nRT, with Pa/kPa/bar/atm and m³/L/cm³/K/°C units.
PV = nRT ｜ R = 8.314 J/(mol·K)Boyle's Law Calculator (P₁V₁=P₂V₂)
In an isothermal process, gas pressure is inversely proportional to volume: given the initial pressure/volume and one final quantity, solve the other (temperature constant).
P₁V₁ = P₂V₂ (isothermal process, T constant)Charles's Law Calculator (V₁/T₁=V₂/T₂)
In an isobaric process, gas volume is proportional to absolute temperature: given any three of the initial/final volume/temperature, solve the fourth (pressure constant).
V₁/T₁ = V₂/T₂ (isobaric process, P constant)Gay-Lussac's Law Calculator (P₁/T₁=P₂/T₂)
In an isochoric process, gas pressure is proportional to absolute temperature: given any three of the initial/final pressure/temperature, solve the fourth (volume constant).
P₁/T₁ = P₂/T₂ (isochoric process, V constant)Specific Heat Calculator (Q=mcΔT)
Compute the heat absorbed or released when an object heats or cools via Q = m·c·ΔT, with results in joules / kilojoules / kilocalories and common material specific-heat references.
Q = m·c·ΔTLatent Heat Calculator (Q=mL)
Compute the heat absorbed or released during a phase change (melting / freezing / vaporization / condensation) via Q = m·L.
Q = m·LHeat Conduction Calculator (Fourier Q=kAΔT/L)
Compute steady heat conduction through a plate/wall via Fourier’s law Q = k·A·ΔT/L, with thermal resistance and heat flux per unit area.
Q = k·A·ΔT / LConvection Calculator (Newton’s Cooling Q=hAΔT)
Compute convective heat transfer between a solid surface and a fluid via Newton’s law of cooling Q = h·A·(Ts − T∞), covering common natural/forced convection coefficients.
Q = h·A·(Ts − T∞)Thermal Radiation Calculator (Stefan–Boltzmann Q=εσAT⁴)
Compute thermal radiation power via the Stefan–Boltzmann law Q = ε·σ·A·T⁴, and enter the surroundings temperature to get net radiative heat transfer.
Q = ε·σ·A·T⁴ ｜ σ = 5.67×10⁻⁸ W/(m²·K⁴)Linear Thermal Expansion Calculator (ΔL=αL₀ΔT)
Compute linear expansion ΔL = α·L₀·ΔT and the expanded length for pipes, structures and precision parts.
ΔL = α·L₀·ΔTVolume Thermal Expansion Calculator (ΔV=βV₀ΔT)
Compute volume expansion ΔV = β·V₀·ΔT and the expanded volume; for solids β ≈ 3α, and liquids use their volume expansion coefficient.
ΔV = β·V₀·ΔT ｜ solid β ≈ 3αMechanical Equivalent of Heat Calculator (W=J·Q)
Convert between heat (calories) and mechanical work (joules): 1 cal = 4.1868 J, for estimating thermal–mechanical energy conversion.
W = J·Q ｜ J = 4.1868 J/calCarnot Efficiency Calculator (η=1−Tc/Th)
Compute the maximum efficiency of an ideal Carnot engine operating between hot reservoir Th and cold reservoir Tc, plus the Carnot refrigerator / heat pump coefficients.
η = 1 − Tc/Th (absolute temperature K)Heat Engine Efficiency Calculator (η=W/Qh)
Compute real heat engine efficiency η = W/Qh: given any two of heat input, heat rejection and work output, solve the third and the efficiency.
η = W / Qh = (Qh − Qc) / QhRefrigeration COP Calculator (COP=Qc/W)
Compute the refrigeration coefficient of performance COP = Qc/W: given cooling capacity and work input, output the COP and heat rejected to the hot side.
COP = Qc / WHeat Pump COP Calculator (COPₕ=Qh/W)
Compute the heat pump coefficient of performance COPₕ = Qh/W: given heating capacity and work input, output the COPₕ and heat absorbed from the cold side.
COPₕ = Qh / W = 1 + Qc/WEntropy Change Calculator (ΔS=Q/T)
Compute entropy change ΔS = Q/T for a reversible isothermal process: enter heat transfer and process temperature to get J/K and kJ/K.
ΔS = Q / T (reversible isothermal process)First Law of Thermodynamics Calculator (ΔU=Q−W)
Solve internal energy change, heat absorbed or work done via the first law ΔU = Q − W (energy conservation).
ΔU = Q − WGas Specific Heat & Adiabatic Index Calculator (γ=Cp/Cv)
Compute the relationship among constant-pressure Cp, constant-volume Cv and adiabatic index γ for an ideal gas, and verify Mayer’s relation Cp−Cv=R.
γ = Cp/Cv ｜ Cp − Cv = RMixture Temperature Calculator (Thermal Equilibrium)
Compute the final temperature when two substances reach thermal equilibrium: m₁c₁(T₁−T) = m₂c₂(T−T₂), with the heat exchanged.
T = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)coulomb定律Calculate器
liang静止点电荷间静电Force：F = k·q1·q2 / r²，同号相斥、异号相吸。
F = k·q1·q2 / r² ｜ k = 1/(4πε0) ≈ 8.988×10⁹ N·m²/C²点电荷电场强度Calculate器
点电荷在空间某点的电场强度：E = k·Q / r²，正电荷向外、负电荷向里。
E = k·Q / r² = F / q ｜ 1 N/C = 1 V/m点电荷电势and电势能Calculate器
点电荷的电势 V = k·Q / r，试探电荷的电势能 U = q·V（标量，带符号）。
V = k·Q / r ｜ U = q·V平行板Capacitance器Calculate器
平行板Capacitance C = εr·ε0·A / d，并给出充电后Electric charge、储能and板间场强。
C = εr·ε0·A / d ｜ Q = C·V ｜ E = ½C·V² ｜ E场 = V / dCapacitance储能Calculate器
Capacitance储存的Energy E = ½·C·V² = ½·Q·V，以及充满时Electric charge。
E = ½·C·V² = ½·Q·V ｜ Q = C·VResistanceandResistance率Calculate器
由Resistance率求导线Resistance R = ρ·L / A，或由Resistance反推材料Resistance率。
R = ρ·L / A ｜ A = π·(d/2)²带电粒子电场加速Calculate器
带电粒子经电势差 U 加速后的Speedand动能：v = √(2·q·U/m)。
v = √(2·q·U / m) ｜ Ek = q·U电Powerand电能Calculate器
直流电路Power P = V·I，and用电时长一start换算电能（J / kWh）。
P = V·I ｜ W = P·t ｜ 1 kWh = 3.6×10⁶ JcurrentandElectric chargeCalculate器
current、Electric chargeandTime互算：I = Q / t，并折算为通过的电子数。
I = Q / t ｜ N = Q / ejoule定律Calculate器
current通过Resistance产生的Heat Q = I²·R·t（joule热），换算为calorie路里。
Q = I²·R·t ｜ 1 cal = 4.184 J直导线磁场Calculate器
无限长载流直导线周围磁感应强度：B = μ0·I / (2πr)。
B = μ0·I / (2πr) ｜ μ0 = 4π×10⁻⁷ N/A²螺线管磁场Calculate器
长直螺线管内部匀强磁场：B = μ0·(N/L)·I，含铁芯时乘 μr。
B = μr·μ0·n·I ｜ n = N/L（turns密度）环形current中心磁场Calculate器
载流Circle环（N turns)Circle心处磁感应强度：B = μ0·N·I / (2R)。
B = μ0·N·I / (2R)洛伦兹ForceCalculate器
带电粒子垂直进入磁场所受洛伦兹Force F = q·v·B，并给出回旋半径andPeriod。
F = q·v·B ｜ r = m·v / (q·B) ｜ T = 2πm / (q·B)ampere培ForceCalculate器
磁场中载流直导线所受ampere培Force：F = B·I·L·sinθ。
F = B·I·L·sinθ磁通量Calculate器
穿过某Area的磁通量 Φ = B·A·cosθ（匀强磁场）。
Φ = B·A·cosθfarad拉第电磁感应Calculate器
磁通量变化产生的感应电动势：ε = N·ΔΦ/Δt（大小）。
ε = N·ΔΦ / Δt动生电动势Calculate器
导体棒在磁场中切割磁感线产生的电动势：ε = B·L·v。
ε = B·L·v（B ⊥ L ⊥ v 时）自感andInductance储能Calculate器
自感系数 L = N·Φ / I，及Inductance储存的磁场能 E = ½·L·I²。
L = N·Φ / I ｜ E = ½·L·I²RL 电路Time常数Calculate器
RL Series电路Time constant τ = L/R，及上电后任意时刻的current。
τ = L/R ｜ i(t) = (V/R)·(1 − e^(−t/τ))芯片发热 / 结温Calculate器
按芯片dissipationand「结 → 壳 → 散热器 → Surroundings」热阻链，Calculate结温、壳温and散热器Temperature，并对比无散热器方案、校核最高结温裕量。
θJA(总) = θJC + θCS + θSA ｜ Tj = Ta + P × θJA ｜ Tc = Tj − P × θJC