Civil Service Math Formulas

Distance

R×T

Rate

D÷T

Time

D÷R

a

a¹

(x+a)(x+b)

x²+bx+ax+ab

1 liter

1000 cm³

1 lb.

16 oz

1 gal.

4 qt

1 qt.

2 pt

1 pt.

2 c

1 cup

8 oz

1 gross

144 units

1 mi.

5280 ft

1 ft.

12 in

3 ft.

1 yd

1 acre

43560 ft²

1 ton

2000 lb

Area of a circle

πr²

Triangle's perimeter

s₁+s₂+s₃

Rectangle's perimeter

2l+2w

Square's perimeter

4s

Square's area

s²

Triangle's area

½bh

Rectangle's area

lw

Pythagorean Theorem

a²+b²=c²

Trapezoid's area

½h(b₁+b₂)

Rhombus/Parallelogram's perimeter

s₁+s₂+s₃+s₄

Rhombus/Parallelogram's area

bh

Cube's surface area

6s²

Circular Cylinder's volume

πr²h

3D Rectangle's volume

lwh

3D Rectangle's surface area

2(lw)+2(hl)+2(wh)

Circular Cylinder's surface area

2πrh+2πr²

Circle's circumference w/ radius

2πr

Circle's circumference w/ diameter

πd

Angles of square's corners

90°

Acute angle

<90°

Right angle

90°

Obtuse angle

>90°

Straight line angle

180°

Circle's angle

360°

pi/π decimal

3.14

pi/π fraction

22/7

Sum of triangle's angles

180°

Sum of square's angles

360°

Sum of rectangles angles

360°

(a¹)²

a¹×²

a¹×a²

a¹⁺²

a¹÷a²

a¹⁻²

(a¹b²)³

a¹×³b²×³

(ab²)³

a³b²×³

f°→c°

(f-32)÷1.8

c°→f°

c×1.8+32

1 in

2.54 cm

Quadratic Equation

ax²+bx+c=0

Quadratic Formula

x=(−b±√b²−4ac)÷2a

Range

x₂-x₁

Slope Intercept (m=slope, b=y-intercept)

y=mx+b

Standard Linear Equation (Solve for x then y)

ax+by=c

slope (y=rise, x=run)

m=y/x

Point Slope (m=slope, y=rise, x=run)

m=(y₂-y₁)÷(x₂-x₁)

Midpoint Formula (solve each side of comma separately)

(x₁+x₂)÷2,(y₁+y₂)÷2