Physics formulas

Divide the change in velocity by time.

Convert wavelength λ into meters. The form accepts nm (default), µm, or m.

Convert aperture diameter D into meters. The form accepts m, cm, or mm.

The Rayleigh criterion for a circular aperture is 1.22 times wavelength divided by diameter.

Convert the angle from radians to arcseconds for astronomy-style quoting.

Divide angle in radians by elapsed time.

Use A = π (D/2)².

Rearrange to solve for P₂ given P₁, densities, velocities, and heights.

Take the arctangent of the refractive-index ratio.

Multiply fluid density, displaced volume, and g.

Enter Charge Q (C) and Voltage V for the Capacitance Calculator; use finite values in the indicated domain. The calculator reports C (F): Capacitance relates stored charge to voltage. Voltage must be nonzero when deriving capacitance from charge.

Compute area from diameter, then multiply by velocity.

Divide mass by volume.

Combine initial-velocity and acceleration contributions over time.

Combine fluid density, speed squared, drag coefficient, and reference area.

Multiply mass by c² (c = 299,792,458 m/s).

Enter Voltage (V) and Current (A) for the Electric Power Calculator; use finite values in the indicated domain. The calculator reports Power (W): Electrical power is voltage times current. Voltage and Current must describe the same operating point; AC circuits may also require power factor.

Multiply mass by acceleration.

Distance is half g t squared; speed is g times t.

Enter Mode (0=f→λ, 1=λ→f), Frequency (Hz), Wavelength (m), and Wave speed (m/s, 0=c) for the Frequency Wavelength Calculator; use only the listed mode or unit codes. The calculator reports Result: v = f λ with speed defaulting to c. Frequency must be positive and Wave speed must use compatible distance/time units.

Multiply μ by normal force.

Divide velocity by the square root of g times characteristic length.

Use G = 6.6743×10⁻¹¹ N·m²/kg².

Enter Spring constant k (N/m) and Displacement x (m) for the Hooke's Law Calculator; use finite values in the indicated domain. The calculator reports Force (N): Hooke's law is linear restoring force for springs. The result applies only within the spring's linear elastic range.

Divide force by area.

For a circle, A/P simplifies to D/4.

Multiply density, gravity, and depth.

Rearrange PV = nRT for the selected variable.

Compute impulse, then Δv = J/m, and add to initial velocity.

Divide the speed of light by the wave speed in the medium.

Half the product of mass and velocity squared.

Divide mean free path by characteristic length.

Scale proper length by the Lorentz factor sqrt term.

Multiply delay by the speed of sound (default 343 m/s).

Divide object speed by the speed of sound.

Take the absolute value of Δv / t.

Multiply incident intensity by cos² of the angle between axes.

Use I = ½ m r² for a uniform solid cylinder or disk.

Multiply mass by acceleration.

Multiply weight by cos of the incline angle.

Rearrange V = I R for the unknown.

Take 2π times the square root of length over g.

Negate the ratio of lateral strain to axial strain.

Multiply mass, gravitational acceleration, and height.

Divide force by area.

Multiply the masses and divide by their sum.

Half the moment of inertia times angular velocity squared.

Enter R1 (Ω), R2 (Ω), and R3 (Ω, 0=skip) for the Series Parallel Resistance Calculator; use finite values in the indicated domain. The calculator reports Series (Ω) and Parallel (Ω): Series adds; parallel uses reciprocal sum. Resistances should be nonnegative, and zero-ohm parallel branches need special handling.

Divide change in length by original length.

Divide applied force by cross-sectional area.

Divide distance by time.

Choose what to solve and the cycle factor S: 2 for a four-stroke (one intake event every two crank revolutions) or 1 for a two-stroke.

Use intake air temperature to estimate the speed of sound, or type a manual C. Dry air at 20 °C is about 343 m/s.

The quarter-wave teaching form sets effective tract length from C, target RPM N, S, and harmonic order O.

Optional: subtract the runner you already have (valve to stack base) and an open-end correction kD to isolate the trumpet contribution.

Multiply force, distance, and cos of the angle between them.