Science calculators

Resolve launch velocity into horizontal and vertical components to estimate projectile range, flight time and height at equal launch and landing elevations.

Science

Free fall from rest

Estimate how long an object dropped from rest takes to fall through a known height and the speed it reaches just before impact.

Science

Escape velocity

Find the minimum escape speed at a specified distance from a central mass, using gravitational potential energy and a zero speed at infinity.

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Circular orbital period

Calculate the time for a circular orbit and its constant orbital speed from the central mass and the centre-to-centre orbital radius.

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Centripetal force

Calculate the inward acceleration and force required to keep a mass moving at a given speed around a circular path of known radius.

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Torque from force

Calculate torque magnitude using force, the distance from the pivot and the angle between them; a parallel force produces no torque.

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Angular momentum

Multiply moment of inertia about a fixed axis by angular velocity to find signed angular momentum; reversing rotation reverses its sign.

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Rotational kinetic energy

Calculate rotational kinetic energy from moment of inertia and the square of angular velocity; rotation direction does not change the energy.

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Spring potential energy

Calculate energy stored in a stretched or compressed spring and the signed restoring force, which acts opposite the entered displacement.

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Mass and spring period

Find the oscillation period and frequency of a mass attached to an ideal spring; a heavier mass slows the oscillation while stiffness speeds it up.

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Simple pendulum period

Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass.

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Hydrostatic pressure

Calculate the pressure increase below the surface of a stationary liquid from density and depth; atmospheric pressure is excluded from this gauge value.

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Ideal hydraulic press

Apply equal fluid pressure to two pistons to find output force and mechanical advantage; the piston areas must use the same square-centimetre unit.

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Pipe flow rate

Multiply the internal cross-sectional area of a circular pipe by mean fluid speed to find volume flow per second and per minute.

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Reynolds number

Compare inertial effects with viscous effects using density, mean speed, characteristic length and dynamic viscosity to obtain a dimensionless Reynolds number.

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Photon energy from wavelength

Convert vacuum wavelength in nanometres into the energy of one photon in joules and electronvolts using Planck’s constant and light speed.

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Net thermal radiation

Estimate net radiated power exchanged with large surroundings from emissivity, surface area and the difference of fourth powers of absolute temperatures.

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Wien peak wavelength

Find the wavelength of maximum blackbody spectral radiance per unit wavelength from absolute temperature; the frequency-spectrum peak is different.

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Inverse square intensity

Estimate intensity at a new distance from an isotropic point source by multiplying the original intensity by the squared distance ratio.

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Thin lens image distance

Use the thin-lens equation to find signed image distance and magnification; a negative image distance represents a virtual image.

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Ideal gas pressure

Calculate gas pressure from amount in moles, absolute temperature and volume using the ideal gas relationship; volume is entered in cubic metres.

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Sensible heat energy

Estimate heat added or removed when a material changes temperature using its mass and specific heat, keeping the sign of the temperature change.

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Linear thermal expansion

Calculate a solid’s change in length and final length from its linear expansion coefficient, original length and signed temperature change.

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Molality

Convert solute mass to moles using molar mass, then divide by kilograms of solvent to obtain molality independently of solution volume.

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Mole fraction of two components

Divide each component’s amount in moles by the total amount to obtain two complementary mole fractions that sum to one.

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Work by a constant force

Calculate mechanical work from force, displacement and their included angle.

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Impulse from force

Find impulse and momentum change from average force over a time interval.

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Hooke’s law

Find the restoring force of a spring from stiffness and signed displacement.

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Sound intensity level

Convert an acoustic intensity and reference intensity into a decibel level.

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Decibel power ratio

Convert a decibel difference into power and equal-impedance amplitude ratios.

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Doppler shift from a moving source

Estimate frequency heard by a stationary observer when a sound source moves toward or away from them.

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Beat frequency

Find the beat rate produced by two nearby frequencies.

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Mach number

Compare object speed to the local speed of sound.

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Gravitational force

Estimate the Newtonian attraction between two point or spherical masses.

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Gravity at a radius

Find gravitational acceleration outside an ideal spherical body.

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Angular acceleration

Find average angular acceleration from initial and final angular velocities.

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Angular displacement

Calculate angular displacement under constant angular acceleration.

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Rolling kinetic energy

Combine translational and rotational energy for an object rolling without slip.

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Heat conduction through a slab

Estimate steady heat conduction through one flat homogeneous layer.

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Carnot efficiency

Find the ideal maximum heat-engine efficiency between two absolute temperatures.

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Heat engine efficiency

Calculate thermal efficiency and rejected heat from heat input and work output.

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Latent heat

Calculate the energy magnitude for a phase change at constant temperature.

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Coulomb force

Estimate electrostatic force between two point charges in vacuum.

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Point-charge electric field

Calculate the radial electric field of a point charge in vacuum.

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Point-charge electric potential

Find the electric potential of a point charge relative to infinity.

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Critical damping coefficient

Find the critical viscous damping coefficient for a single mass-spring oscillator.

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Convective heat transfer coefficient

Infer an average convective heat-transfer coefficient from heat flow, area and temperature difference.