SAT Math Formulas

What the test hands you, and what you have to bring yourself. Two lists, nothing else.

Given on test day

This mirrors the official reference sheet you'll have in Bluebook — one tap away on test day.

Reference sheet

  • Area of a circle

    A=πr2A = \pi r^2

  • Circumference of a circle

    C=2πrC = 2\pi r

  • Area of a rectangle

    A=lwA = lw

  • Area of a triangle

    A=12bhA = \tfrac{1}{2}bh

  • Pythagorean theorem

    c2=a2+b2c^2 = a^2 + b^2

  • 30-60-90 triangle

    x, x3, 2xx,\ x\sqrt{3},\ 2x

  • 45-45-90 triangle

    s, s, s2s,\ s,\ s\sqrt{2}

  • Volume of a box

    V=lwhV = lwh

  • Volume of a cylinder

    V=πr2hV = \pi r^2 h

  • Volume of a sphere

    V=43πr3V = \tfrac{4}{3}\pi r^3

  • Volume of a cone

    V=13πr2hV = \tfrac{1}{3}\pi r^2 h

  • Volume of a pyramid

    V=13lwhV = \tfrac{1}{3}lwh

  • Circle & triangle facts

    A circle has 360° = 2π radians of arc. The angles of a triangle sum to 180°.

Know by heart — not provided on the test

Linear equations & graphs

  • Slope

    m=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}

  • Slope-intercept form

    y=mx+by = mx + b

  • Point-slope form

    y−y1=m(x−x1)y - y_1 = m(x - x_1)

  • Parallel & perpendicular lines

    Parallel lines have equal slopes. Perpendicular lines: m₁·m₂ = −1.

  • Distance between two points

    d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

  • Midpoint

    (x1+x22, y1+y22)\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)

  • Absolute value equations

    ∣x∣=a  ⇒  x=a or x=−a(a≥0)|x| = a \;\Rightarrow\; x = a \text{ or } x = -a \quad (a \ge 0)

  • How many solutions a linear system has

    Different slopes → one solution. Same slope, different intercepts → none. Same line → infinitely many.

Quadratics & polynomials

  • Difference of squares

    a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b)

  • Square of a sum / difference

    (a±b)2=a2±2ab+b2(a \pm b)^2 = a^2 \pm 2ab + b^2

  • Quadratic formula

    x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

  • Discriminant

    D=b2−4acD = b^2 - 4ac

    D > 0: two real roots. D = 0: one. D < 0: none.

  • Vertex of a parabola

    x=−b2a;y=a(x−h)2+kx = -\dfrac{b}{2a};\quad y = a(x-h)^2 + k

  • Factored form & roots

    y=a(x−p)(x−q)y = a(x-p)(x-q)

    has roots p and q

  • Sum & product of roots (Vieta)

    x1+x2=−ba,x1x2=cax_1 + x_2 = -\dfrac{b}{a},\quad x_1 x_2 = \dfrac{c}{a}

Exponents, radicals & exponential change

  • Product of powers

    am⋅an=am+na^m \cdot a^n = a^{m+n}

  • Quotient of powers

    aman=am−n\dfrac{a^m}{a^n} = a^{m-n}

  • Power of a power

    (am)n=amn(a^m)^n = a^{mn}

  • Negative & zero exponents

    a−n=1an;a0=1 (a≠0)a^{-n} = \dfrac{1}{a^n};\quad a^0 = 1 \ (a \ne 0)

  • Fractional exponents

    am/n=amna^{m/n} = \sqrt[n]{a^m}

  • Product of radicals

    ab=ab(a,b≥0)\sqrt{ab} = \sqrt{a}\sqrt{b} \quad (a,b \ge 0)

  • Exponential growth & decay

    y=a(1+r)t/y=a(1−r)ty = a(1+r)^t \quad\text{/}\quad y = a(1-r)^t

  • Function shifts

    f(x−h)+kf(x-h)+k

    shifts the graph h units right and k units up

Percentages, ratios & data

  • Percent of a number

    x% of y=x100⋅yx\%\text{ of }y = \dfrac{x}{100}\cdot y

  • Percent change

    new−oldold×100%\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%

  • Mean (average)

    mean=sumcount\text{mean} = \dfrac{\text{sum}}{\text{count}}

  • Median & range

    Median = middle value of the sorted data. Range = max − min.

  • Proportions (cross-multiply)

    ab=cd  ⟺  ad=bc\dfrac{a}{b} = \dfrac{c}{d} \iff ad = bc

  • Probability

    P=favorabletotalP = \dfrac{\text{favorable}}{\text{total}}

Trigonometry & circles

  • SOH-CAH-TOA

    sin⁡=opphyp, cos⁡=adjhyp, tan⁡=oppadj\sin = \dfrac{\text{opp}}{\text{hyp}},\ \cos = \dfrac{\text{adj}}{\text{hyp}},\ \tan = \dfrac{\text{opp}}{\text{adj}}

  • Pythagorean identity

    sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1

  • Complementary angles

    sin⁡x=cos⁡(90°−x)\sin x = \cos(90° - x)

  • Degrees to radians

    radians=degrees×π180\text{radians} = \text{degrees} \times \dfrac{\pi}{180}

  • Equation of a circle

    (x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

  • Arc length & sector area

    arc2πr=sectorπr2=angle360°\dfrac{\text{arc}}{2\pi r} = \dfrac{\text{sector}}{\pi r^2} = \dfrac{\text{angle}}{360°}

Knowing a formula and using it under time pressure are different skills. Practice SAT Math to build the second one.