Unit of Measure Conversions
Angles in Regular n-sided Polygons
| Parameter | Formula |
|---|---|
| Internal angle between adjacent sides | 180(n-2)/n |
| Sum of all internal angles | 180(n-2) |
Properties of Geometric Shapes
| Shape | Circumference | Surface Area | Volume |
|---|---|---|---|
| Circle | 2πr [or: πd] | πr² [or: πd²/4] | |
| Cone | πrs | πr²h/3 | |
| Cube | 4b | 6b² | b³ |
| Cylinder (hollow) | 2πro [or: 2πri] | 2π{h(ro+ri)+(ro²-ri²)} | πh(ro²-ri²) |
| Cylinder (solid) | 2πr [or: πd] | 2πr(h+r) [or: πd(h+r)] | πr²h |
| Ellipse | Reference | πxy | |
| Parallelogram, Rhombus | 2(b+s) | bh | |
| Polygon (regular) | kb | kp²sin(360/k)/2 | |
| Pyramid (regular) | kb | A+(kbs/2) | Ah/3 |
| Rectangle | 2(b+h) | bh | |
| Sphere | 2πr [or: πd] | 4πr² [or: πd²] | 4πr³/3 |
| Square | 4b | b² | |
| Trapezium | a+b+2s | (a+b)h/2 | |
| Triangle | b+t2+t3 | bh/2 | |
| Triangle (equilateral) | 3b | (√3)b²/4 [or: bh/2] |
Key:
| Symbol | Description |
|---|---|
| π | Pi |
| A | Area of base |
| a | Length of side parallel to baseline |
| b | Length of baseline |
| d | Diameter |
| h | Vertical height |
| k | Number of sides |
| p | Length from centre to a corner |
| r,ro,ri | Radius, outer radius, inner radius |
| s | Slant height |
| t2,t3 | Length of sides other than baseline |
| x | Half length of major axis |
| y | Half length of minor axis |
Regular Polyhedra
A polyhedron is a solid (3-D) figure with polygons for its faces.
All faces of a regular polyhedron are the same in every respect - there are just five types.
| Name | Composition |
|---|---|
| Tetrahedron | 4 triangular faces |
| Cube | 6 square faces |
| Octahedron | 8 triangular faces |
| Dodecahedron | 12 pentagonal faces |
| Icosahedron | 20 triangular faces |
Combinations and Permutations
Combinations
The number of ways of drawing "r" different objects from a larger set of "n" objects,
with no regard to the order in which they are drawn, is expressed as nCr.
| nCr = n!/(r!(n-r)!) |
where ! = Factorial (see the Tips page for definition)
Permutations
The number of ways of drawing "r" different objects from a larger set of "n" objects,
paying attention to the order in which they are drawn, is expressed as nPr.
| nPr = n!/(n-r)! |
Gas Consumption (UK)
To convert gas consumption into kilowatt-hours use the formula:
| Gas kWh = ((CR-PR)⋅VC⋅CV)/3.6 |
where
- CR = Current gas meter Reading
- CV = Supplier's gas Calorific Value (approx 39.2)
- PR = Previous gas meter Reading
- VC = Supplier's Volume Correction number (approx 1.02264)
If necessary, multiply the result by 2.83 if the readings came from an Imperial meter that measures gas consumption in 100's of cubic feet rather than cubic metres.
Equations of Motion
These apply to objects moving with uniform acceleration.
| v = u+at |
| s = ut+at²/2 |
| s = (u+v)t/2 |
| v² = u²+2as |
where
- a = Acceleration
- s = Distance
- t = Time
- u = Initial velocity
- v = Final velocity
Simple Pendulum
The formula to calculate the time taken for one complete swing (T) holds true provided that:
- The angle of swing is small
- The string/wire has negligible mass
- The mass of the bob is concentrated at one point
- The friction at the point of suspension is neglected
| T = 2π√(L/g) |
where
- g = Acceleration due to gravity (see the Useful Numbers page for value)
- L = Length of the string/wire
Projectile Trajectories
These formulae hold true provided that air resistance is neglected.
| Parameter | Formula |
|---|---|
| Horizontal range | (v²⋅sin2θ)/g |
| Maximum height | (v²⋅sin²θ)/2g |
| Time to reach maximum height | (v⋅sinθ)/g |
| Total flight time | (2v⋅sinθ)/g |
where
- θ = Angle of discharge from horizontal
- g = Acceleration due to gravity (see the Useful Numbers page for value)
- v = Discharge velocity
Temperature Scale Conversions
| Conversion | Formula |
|---|---|
| Celsius to Fahrenheit | °F = 1.8°C+32 |
| Fahrenheit to Celsius | °C = (°F-32)/1.8 |
| Celsius to Kelvin | K = °C+273.15 |
| Kelvin to Celsius | °C = K-273.15 |
See also the Temperature Scale Conversions page.