Rectangle area
length × width
A 12 ft by 15 ft pad is 180 square feet. Adding the sides is not area.
Formula sheet
The conversions and relationships the guide says to know cold. Same rules the drills use.
Units
LearnFormulas
Square area
side × side
An 11 ft square is 121 square feet. The perimeter is 44 feet.
Box volume
length × width × height
Answer in cubic units. A 4 × 3 × 2 ft crate is 24 cubic feet.
Radius and diameter
radius = diameter ÷ 2
Diameter crosses the whole circle. Radius stops at the center.
Circumference
π × diameter
The distance around. About 3.14 × diameter. A 10-inch diameter is about 31.4 inches around. Do not use the radius unless you double it first.
Percent of a number
percent ÷ 100, then multiply
15% of 260: 10% is 26 and 5% is 13, so 39.
Ratio
a:b means a of the first for every b of the second
A 4:1 reduction turns the output once for four turns of the input. 800 RPM in is 200 RPM out.
Proportion
scale both numbers by the same factor
If 5 bolts weigh 10 oz, 15 bolts weigh 30 oz. On a sketch, 1/4 inch = 1 foot means 2 inches = 8 feet.
Average
add the values, divide by how many
The total and the average are different answers. Read which one is asked.
Flow
volume = rate × time
Time = volume ÷ rate. Keep gallons with gallons, minutes with minutes.
Order of operations
parentheses, then × and ÷ left to right, then + and − left to right
The guide calls this PEMDAS. Multiply does not always come before divide.
Lever
advantage = effort arm ÷ load arm
Effort = load ÷ advantage. A longer handle means less force and more distance.
Pro-Tip. A first-class lever is a seesaw. The fulcrum is in the middle. The longer side needs less force.
Seesaw
weight × distance matches on both sides
The heavier person sits closer to the fulcrum.
Pro-Tip. Heavier sits closer. The longer side needs less weight to balance.
Pulley
advantage ≈ number of rope parts holding the load
A fixed pulley is 1. You pull more rope than the load rises.
Pro-Tip. Count the ropes holding the load. More ropes, less pull.
Gears
teeth × RPM is the same for both gears
Fewer teeth means faster RPM. Meshed gears turn opposite ways.
Pro-Tip. Fewer teeth, faster spin. The other gear turns the opposite way.
Wheel and axle
advantage = wheel radius ÷ axle radius
A big handwheel is easier. Your hand travels farther.
Pro-Tip. A bigger handle is an easier turn. Your hand just travels farther.
Ramp
advantage = slope length ÷ height
A longer ramp to the same height takes less effort.
Pro-Tip. A longer ramp to the same height is an easier push.
Work and speed
work = force × distance moved · speed = distance ÷ time
No movement means no work done on the part. Linear speed is along the path.
Buoyancy
upward force = weight in air − weight underwater
That force equals the weight of the fluid pushed aside.
Pro-Tip. The scale reads light underwater by the weight of the water pushed aside.
Shapes
LearnTerms
For each one, ask what it does, what changes it, and where you meet it on a job.
- How many times a machine multiplies your force. You pay it back in distance.
- A push or a pull. Unbalanced forces change motion.
- Force times the distance the object moves in that direction.
- The pull of gravity on an object.
- The attraction that gives an object its weight and makes it fall.
- Speed with a direction.
- Distance traveled along a path divided by time.
- Resistance to sliding. Rougher surfaces and more weight increase it.
- The outward feeling in a turn. Let go, and the object goes straight on the tangent.
- The bar turns on a fulcrum. Effort is the force you apply.
- On a lever, heavier weight must sit closer to the fulcrum to balance.
- Wheels and rope. A fixed pulley redirects the pull. More supporting ropes raise the advantage.
- Teeth times RPM matches on meshed gears. The smaller gear spins faster.
- A dropped object speeds up as it falls, until air resistance balances its weight.
- Sideways motion and falling happen together. Sideways speed does not hold the object up.
- A longer swing takes more time. The bob’s weight does not set the time.
- Heat moves from the hotter object to the cooler one until they even out.
- Volume per time, such as gallons per minute.
- Weight divided by volume. It decides sinking and floating against the fluid.
- The upward force from a fluid, equal to the weight of fluid pushed aside.
- A part out of 100. Of means multiply by the decimal.
- Tenths are one place past the point. Hundredths are two.
- The total divided by the count.
- Parentheses, then multiply and divide left to right, then add and subtract left to right.
- Thin blades of known thickness used to measure a small gap.
- Read the mark at the edge, including the fraction of an inch.
- A closed loop from the battery, through the load, and back.
- The flow around a closed circuit. No loop, no flow.
- A break in the loop, such as a pushbutton that is up. The bulb stays dark.
- A path around the load. Current skips the bulb, so the bulb does not light.
- One path through every bulb. Open any one and the others go dark.
- Each bulb has its own path. One can be dark while another stays lit.
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The guide also points at these. Books it names, if you want paper: Master the Civil Service Exams (synonyms, fractions, percents), Barron’s Mechanical Aptitude, How2Become Mechanical Comprehension, and the Mometrix mechanical aptitude guide. Search “free ASVAB practice” for extra verbal and math.
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