GATE Biomedical Engineering (BM) Calculators
Calculators for the numerical questions in GATE Biomedical Engineering: circuits and signals, bioinstrumentation, physiology, medical imaging and biomechanics, each showing the working.
41 calculators · 5 converters · common conversions
Engineering Mathematics
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Eigenvalue Calculator
det(A − λI) = 0
Σλ = trace A, Πλ = det A
Example: The matrix [[4, 1], [2, 3]]: Eigenvalues: λ₁ = 5, λ₂ = 2.
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Normal Distribution Calculator
z = (x − μ)/σ, P(X < x) = Φ(z)
Φ standard normal cumulative distribution
Example: X normal with μ = 50 and σ = 10, between 40 and 65: P(40 < X < 65) = 0.7745375448.
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- Bayes’ Theorem Calculator – Priors and likelihoods → total probability and posterior probabilities, with a Bayes table.
- Standard Deviation Calculator – Paste a list of numbers → standard deviation, variance, mean, median, MAD and CV with steps.
- Correlation & Regression Calculator – Paste x and y values → correlation r, R², slope, intercept and regression equation.
- Numerical Integration Calculator – f(x), limits and intervals → trapezoidal, Simpson 1/3 and 3/8 results with a reference value.
- Newton-Raphson Method Calculator – f(x), optional f′(x) and a starting guess → root, iteration table and convergence check.
Electrical Circuits
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Ohm's Law Calculator
V = I R, P = V I
V voltage, I current, R resistance, P power
Example: 12 V across 4 Ω drives 3 A and dissipates 36 W.
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Voltage Divider Calculator
Vₒᵤₜ = Vᵢₙ R₂ / (R₁ + R₂)
with a load R_L across R₂, replace R₂ by R₂∥R_L; current divider: I₁ = I R₂/(R₁ + R₂)
Example: 12 V across R₁ = 10 kΩ and R₂ = 4.7 kΩ, unloaded: Output voltage Vₒᵤₜ = 3.83673 V.
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- RC & RL Time Constant Calculator – R and C (or L) → time constant and the voltage or current at any time t.
- RLC Resonance Calculator – R, L and C → resonant frequency, Q, bandwidth, half-power points and damping.
- Impedance Calculator – R, L, C and frequency → impedance magnitude, rectangular form, phase and power factor.
- RMS Value Calculator – Waveform and peak value → RMS, average, form factor and crest factor.
- AC Power Calculator – Voltage, current and power factor → kW, kVA, kVAR and complex power.
Signals and Systems
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Sampling Theorem Calculator
fₛ ≥ 2f_max
alias frequency f_a = |f − k fₛ| with k the nearest integer to f/fₛ
Example: A 4 kHz signal sampled at 6 kHz, and a 5 kHz tone in the same system: Nyquist rate 2f_max = 8 kHz.
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DFT Calculator
X[k] = Σ x[n] e^(−j2πkn/N)
k = 0 … N − 1; X[0] is the sum of the samples
Example: The 4-point sequence x[n] = {1, 2, 3, 4}: X[0] (sum of the samples) = 10.
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Convolution Calculator
y[n] = Σₖ x[k] h[n − k]
length of linear convolution = L_x + L_h − 1; circular wraps modulo N
Example: x[n] = {1, 2, 3} through h[n] = {1, 1, 1}: Linear convolution y[n] = {1, 3, 6, 5, 3}.
Analog and Digital Electronics
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Op-Amp Gain Calculator
Inverting −R_f/Rᵢₙ, non-inverting 1 + R_f/Rᵢₙ
difference (R_f/Rᵢₙ)(V₂ − V₁); in-amp 1 + 2R/R_G; summing −(R_f/Rᵢₙ)ΣV
Example: An inverting amplifier with Rᵢₙ = 10 kΩ, R_f = 100 kΩ and 0.2 V in: Voltage gain = -10.
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ADC Resolution Calculator
LSB = Vref / 2ⁿ, SNR = 6.02n + 1.76 dB
code = floor(Vᵢₙ/LSB); ENOB = (SINAD − 1.76)/6.02
Example: A 12-bit ADC with a 3.3 V reference converting 1.65 V: Resolution (1 LSB) = 0.805664 mV.
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- 555 Timer Calculator – Resistors and capacitor → astable frequency and duty cycle, or monostable pulse width.
- Number Base Converter – A number in any base 2–36 → binary, octal, decimal and hex, with fractional parts.
- K-Map Solver – Minterms and don’t-cares → minimal sum of products, product of sums, prime and essential implicants.
Measurements and Control Systems
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Error Propagation Calculator
Sums: ΔA + ΔB; products: ΔA/A + ΔB/B
powers: Δy/y = |n| ΔA/A; statistical errors combine as √(Σ squares)
Example: A = 100 ± 1 and B = 20 ± 0.4 multiplied, limiting errors: Result y = 2000 ± 60.
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Wheatstone Bridge Calculator
Rₓ = R₂R₃ / R₁ at balance
Vₒᵤₜ = V_s [R₂/(R₁ + R₂) − Rₓ/(R₃ + Rₓ)]
Example: A bridge with equal 1 kΩ ratio arms balanced with R₃ = 470 Ω: Unknown resistance Rₓ = 470 Ω.
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Second-Order System Calculator
Mₚ = e^(−ζπ/√(1−ζ²)), tₚ = π/ω_d
ω_d = ωₙ√(1 − ζ²), t_r = (π − arccos ζ)/ω_d, t_s ≈ 4/(ζωₙ) (2 %)
Example: A system with ζ = 0.5 and ωₙ = 4 rad/s (s² + 4s + 16): Peak overshoot Mₚ = 16.3034 %.
Sensors and Bioinstrumentation
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Strain Gauge Calculator
ΔR/R = GF × ε
quarter bridge Vₒ ≈ V_ex GF ε / 4; half (bending) V_ex GF ε/2; full V_ex GF ε
Example: A 350 Ω gauge, GF = 2, at 1000 µε in a quarter bridge with 5 V excitation: Bridge output Vₒᵤₜ = 2.4975 mV.
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RTD Calculator
R = R₀(1 + AT + BT²) for T ≥ 0 °C
A = 3.9083 × 10⁻³, B = −5.775 × 10⁻⁷; below 0 °C add C(T − 100)T³, C = −4.183 × 10⁻¹²
Example: A Pt100 at 100 °C: Resistance R = 138.5055 Ω.
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- Thermistor Calculator – Nominal resistance, B constant and temperature ↔ thermistor resistance.
- ECG Heart Rate Calculator – R–R interval or squares between beats → heart rate and corrected QT.
- Cardiac Output Calculator – Stroke volume and heart rate, or Fick data → cardiac output, BSA and cardiac index.
- Mean Arterial Pressure Calculator – Systolic and diastolic pressure → mean arterial pressure and pulse pressure.
- Nernst Equation Calculator – Ion, concentrations and temperature → equilibrium (Nernst) potential.
Medical Imaging Systems
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X-Ray Attenuation Calculator
I = I₀ e^(−μx)
μ linear attenuation coefficient; HVL = ln 2/μ; TVL = ln 10/μ
Example: A beam through 6.93 cm of soft tissue with μ = 0.2 cm⁻¹: Transmitted intensity I = 25.0074.
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Larmor Frequency Calculator
f = (γ/2π) B₀
γ/2π for ¹H = 42.577478518 MHz/T (CODATA 2018)
Example: Hydrogen nuclei (protons) in a 1.5 T scanner: Larmor frequency f = 63.8662 MHz.
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- Doppler Ultrasound Calculator – Transmit frequency, angle and velocity ↔ Doppler shift.
- Photon Energy Calculator – Wavelength, frequency or energy → the other two, per photon and per mole.
- Half-Life Calculator – Initial amount, half-life and time → amount left; or the age, half-life or starting amount.
Biomechanics
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Tensile Stress Calculator
σ = F ÷ A
σ normal stress, F axial force, A cross-sectional area
Example: 10 kN on a 10 mm bar = 127.3 MPa.
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Young's Modulus Calculator
E = σ ÷ ε
E Young's modulus, σ stress, ε strain = ΔL ÷ L₀
Example: 250 MPa at 0.125 % strain gives E = 200 GPa.
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- Hooke's Law Calculator – Any two of spring force, spring constant and extension → the third, plus stored energy.
- Poiseuille Flow Calculator – Radius, length, viscosity and pressure difference → laminar flow rate; or the pressure or radius.
Unit Converters for GATE Biomedical (BM)
- Pressure Converter – Pa, kPa, psi, bar, inH₂O, mmHg, torr, atm
- Flow Rate Converter – CFM, m³/h, L/min, L/s, GPM, sccm, SLPM
- Temperature Converter – °C, °F, K, °R
- Frequency & RPM Converter – Hz, kHz, MHz, GHz, rpm, rad/s
- Length Converter – m, km, cm, mm, µm, ft, in, mi, yd, nmi
Common GATE Biomedical (BM) Conversions
How to use these GATE Biomedical calculators
GATE Biomedical Engineering combines electrical engineering with physiology and medical imaging. Besides the shared circuit, signal, electronics and measurement tools, this hub collects calculators for cardiac output by stroke volume and by the Fick principle, mean arterial pressure, heart rate and corrected QT from ECG intervals, the Nernst potential of ions, Poiseuille flow in vessels, X-ray attenuation and half-value layers, the MRI Larmor frequency and the Doppler ultrasound equation.
These are study and checking tools that apply the textbook equations with stated constants: CODATA values for physical constants, 1540 m/s for sound in soft tissue, and the Mosteller formula for body surface area. They do not interpret clinical measurements.
Solve each question by hand first, then confirm it here. Physiology questions often hide unit traps, such as millilitres per decilitre in the Fick equation or milliseconds versus seconds in QT correction, and the step-by-step working makes those visible.