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Percentage Table
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.333...% |
| 2/3 | 0.666... | 66.666...% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.1666... | 16.666...% |
| 5/6 | 0.8333... | 83.333...% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| Fraction | Decimal | Percent |
|---|---|---|
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/9 | 0.111... | 11.111...% |
| 2/9 | 0.222... | 22.222...% |
| 4/9 | 0.444... | 44.444...% |
| 5/9 | 0.555... | 55.555...% |
| 7/9 | 0.777... | 77.777...% |
| 8/9 | 0.888... | 88.888...% |
| 1/10 | 0.1 | 10% |
| 1/12 | 0.08333... | 8.333...% |
| 1/16 | 0.0625 | 6.25% |
| 1/32 | 0.03125 | 3.125% |
| 1/50 | 0.02 | 2% |
Percentages Formulas
Y = P% * X
WHAT is P% of X?
Ex: What is 25% of 150?
Y is 25% of 150
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 25% * 150
Converting percent to decimal:
p = 25%/100 = 0.25
Y = 0.25 * 150
Y = 37.5
Y is WHAT Percent of X?
35 is what percent of 175?
35 is P% of 175
Equation: Y = P% * X
Solving our equation for P
P% = Y/X
P% = 35/175
p = 0.2
Convert decimal to percent:
P% = 0.2 * 100 = 20%
Y is P% of WHAT?
35 is 12% of what?
35 is 12% of X
Equation: Y = P% * X
Solving our equation for X
X = Y/P%
X = 35/12%
Converting percent to decimal:
p = 12%/100 = 0.12
X = 35/0.12
X = 291.6667
P% * X = Y
WHAT % of X is Y?
Ex: What % of 2400 is 360?
P% of 2400 is 360
Equation: P% * X = Y
Solving our equation for P
P% = Y/X
P% = 360/2400
p = 0.15
Convert decimal to percent:
P% = 0.15 * 100 = 15%
P% of What is Y Calculator?
35% of what is 560?
35% of X is 560
Equation: P% * X = Y
Solving our equation for X
X = Y/P%
X = 560/35%
Converting percent to decimal:
p = 35%/100 = 0.35
X = 560/0.35
X = 1600
Ex: P% of X is What Calculator?
32% of 560 is what?
32% of 560 is Y
Equation: P% * X = Y
Solving our equation for Y
Y = P% * X
Y = 32% * 560
Converting percent to decimal:
p = 32%/100 = 0.32
Y = 0.32 * 560
Y = 179.2
Y ÷ X= P%
Ex: Y out of What is P% Calculator?
350 out of what is 15%?
350 out of X is 15%
Equation: Y/X = P%
Solving our equation for X
X = Y/P%
X = 350/15%
Converting percent to decimal:
p = 15%/100 = 0.15
X = 350/0.15
X = 2333.3333
Ex: What out of X is P% Calculator?
What out of 450 is 12%?
Y out of 450 is 12%
Equation: Y/X = P%
Solving our equation for Y
Y = P% * X
Y = 12% * 450
Converting percent to decimal:
p = 12%/100 = 0.12
Y = 0.12 * 450
Y = 54
Ex: Y out of X is WHAT Percent Calculator?
570 out of 850 is what %?
570 out of 850 is P%
Equation: Y/X = P%
Solving our equation for P
P% = Y/X
P% = 570/850
p = 0.6706
Convert decimal to percent:
P% = 0.6706 * 100 = 67.06%
X + (X × P%) = Y
Ex: X plus P% is WHAT?
Ex: What is 25% of 150?
350 plus 12% is what?
350 plus 12% is Y
Equation:
X + (X × P%) = Y
X(1 + P%) = Y
Solving our equation for Y
Y = X(1 + P%)
Y = 350(1 + 12%)
Converting percent to decimal:
p = 12%/100 = 0.12
Y = 350(1 + 0.12)
Y = 350(1.12)
Y = 392
Ex: X plus WHAT Percent is Y?
420 plus what % is 560?
420 plus P% is 560
Equation:
X + (X × P%) = Y
X(1 + P%) = Y
Solving our equation for P
P% = Y/X - 1
P% = 560/420 - 1
p = 0.3333
Convert decimal to percent:
P% = 0.3333 * 100 = 33.33%
Ex: What plus P% is Y?
What plus 25% is 450?
X plus 25% is 450
Equation:
X + (X × P%) = Y
X(1 + P%) = Y
Solving our equation for X
X = Y/(1 + P%)
X = 450/(1 + 25%)
Converting percent to decimal:
p = 25%/100 = 0.25
X = 450/(1 + 0.25)
X = 450/1.25
X = 360
X - (X × P%) = Y
Ex: X minus P% is WHAT?
450 minus 12% is what?
450 minus 12% is Y
Equation:
X - (X × P%) = Y
X(1 - P%) = Y
Solving our equation for Y
Y = X(1 - P%)
Y = 450(1 - 12%)
Converting percent to decimal:
p = 12%/100 = 0.12
Y = 450(1 - 0.12)
Y = 450(0.88)
Y = 396
Ex: X minus WHAT Percent is Y?
650 minus what % is 325?
650 minus P% is 325
Equation:
X - (X × P%) = Y
X(1 - P%) = Y
Solving our equation for P
P% = 1 - Y/X
P% = 1 - 325/650
p = 0.5
Convert decimal to percent:
P% = 0.5 * 100 = 50%
Ex: WHAT minus P% is Y?
What minus 2% is 490?
X minus 2% is 490
Equation:
X - (X × P%) = Y
X(1 - P%) = Y
Solving our equation for X
X = Y/(1 - P%)
X = 490/(1 - 2%)
Converting percent to decimal:
p = 2%/100 = 0.02
X = 490/(1 - 0.02)
X = 490/0.98
X = 500
Percentage Change Formula
Percentage Change = [ (New_Value - Original_Value) / |Original_value| ] * 100
Ex: Percentage Change from 250 to 350?
Solution: New_Value = 350, Original_Value = 250
Percentage Change = [ (New_Value - Original_Value) / |Original_value| ] * 100
Substitute the given values in the formula.
Percentage Change = (350 - 250) / |250| * 100
Percentage Change = (100/250) * 100 = (2/5) * 100 = 0.4 * 100
Percentage Change = 40%
∴ Percentage Change from 250 to 350 is 40%
Percent Error Formula
percent error = [ (AV - OV) / | AV | ] * 100%
where: AV is the actual value, and OV is the observed value.
Ex: Percent Error from 200 to 250?
Solution: actual value = 200, observed value = 250
Percent Error = [ (AV - OV) / | AV | ] * 100%
Substitute the given values in the formula.
Percent Error = (250 - 200) / |200| * 100
Percent Error = (50/200) * 100 = (1/4) * 100 = 0.25 * 100
Percent Error = 25%
∴ Percent Error from 200 to 250 is 25%
Percentage Increase Formula
Percentage Increase = [ (FV - SV) / | SV | ] * 100%
where: FV is the final value, and SV is the starting value.
Ex: Percent Increase from 90 to 108?
Solution: Starting Value = 90, Final Value = 108
Percentage Increase = [ (FV - SV) / | SV | ] * 100%
Substitute the given values in the formula.
Percentage Increase = (108 - 90) / |90| * 100
Percentage Increase = (18/90) * 100 = (1/5) * 100 = 0.2 * 100
Percentage Increase = 20%
∴ Percent Increase from 90 to 108 is 20%
Percentage Decrease Formula
Percentage Decrease = [ (SV - FV) / | SV | ] * 100%
where: FV is the final value, and SV is the starting value.
Ex: Percent Decrease from 80 to 68?
Solution: Starting Value = 80, Final Value = 68
Percentage Increase = [ (SV - FV) / | SV | ] * 100%
Substitute the given values in the formula.
Per. Decrease = (80 - 68) / |80| * 100
Per. Decrease = (12/80) * 100 = (3/20) * 100 = 0.15 * 100
Per. Decrease =
∴ Percent Decrease from 80 to 68 is 15%
Percentage Difference Formula
Percentage Difference = 100 * |a - b| / ((a + b) / 2)
Ex: Percent Difference from 300 to 200?
Solution: a = 300, b = 200
Percentage Difference = 100 * |a - b| / ((a + b) / 2)%
Substitute the given values in the formula.
Percentage Difference = 100 * |300 - 200| / ((300+200) / 2)%
P.D = 100 * |100| / (500/2)
P.D = (10000 / 250)%
P.D = 40%
∴ Percent Difference from 300 to 200 is 40%
Percentage of a Percentage Formula
Percentage of a Percentage = (pct1 ÷ 100) × (pct2 ÷ 100) × 100
where: pct1 is the percentage 1, and pct2 is the percentage 2.
Ex: Find 25% of 60%
Solution: pct1 = 300, pct2 = 200
p = (pct1 ÷ 100) × (pct2 ÷ 100) × 100
p = (25 ÷ 100) × (60 ÷ 100) × 100
p = .25 × .6 × 100
p = .15 × 100
p = 15%
∴ 25% of 60% is 15%
Doubling Time Formula
doubling time = log(2) / log(1 + r)
Where: r = a constant growth rate
| Growth Rate | Doubling Time |
|---|---|
| 0.1 | 693.49 |
| 0.2 | 346.92 |
| 0.3 | 231.4 |
| 0.4 | 173.63 |
| 0.5 | 138.98 |
| 0.6 | 115.87 |
| 0.7 | 99.36 |
| 0.8 | 86.99 |
| 0.9 | 77.36 |
| 1 | 69.66 |
| 1.1 | 63.36 |
| 1.2 | 58.11 |
| 1.3 | 53.66 |
| 1.4 | 49.86 |
| 1.5 | 46.56 |
| 1.6 | 43.67 |
| 1.7 | 41.12 |
| 1.8 | 38.85 |
| 1.9 | 36.83 |
| 2 | 35 |
| Growth Rate | Doubling Time |
|---|---|
| 2.1 | 33.35 |
| 2.2 | 31.85 |
| 2.3 | 30.48 |
| 2.4 | 29.23 |
| 2.5 | 28.07 |
| 2.6 | 27 |
| 2.7 | 26.02 |
| 2.8 | 25.1 |
| 2.9 | 24.25 |
| 3 | 23.45 |
| 3.1 | 22.7 |
| 3.2 | 22.01 |
| 3.3 | 21.35 |
| 3.4 | 20.73 |
| 3.5 | 20.15 |
| 3.6 | 19.6 |
| 3.7 | 19.08 |
| 3.8 | 18.59 |
| 3.9 | 18.12 |
| 4 | 17.67 |
| Growth Rate | Doubling Time |
|---|---|
| 4.1 | 17.25 |
| 4.2 | 16.85 |
| 4.3 | 16.46 |
| 4.4 | 16.1 |
| 4.5 | 15.75 |
| 4.6 | 15.41 |
| 4.7 | 15.09 |
| 4.8 | 14.78 |
| 4.9 | 14.49 |
| 5 | 14.21 |
| 5.5 | 12.95 |
| 6 | 11.9 |
| 6.5 | 11.01 |
| 7 | 10.24 |
| 7.5 | 9.58 |
| 8 | 9.01 |
| 8.5 | 8.5 |
| 9 | 8.04 |
| 9.5 | 7.64 |
| 10 | 7.27 |
Convert Fraction to Percentage
Simple Formula to Convert Fraction to Percent
(n / d) * 100 = P
where n is the numerator, d is the denominator, and p is the percentage.
Percentages Calculators 💯
- Percentage Calculator
- Percent error Calculator
- Percentage change Calculator
- Percentage increase Calculator
- Percentage difference Calculator
- Doubling time Calculator
- Convert fraction to percentage Calculator
- Percentage decrease Calculator
- Percentage of a percentage Calculator
Arithmetic calculators ➗
- Average Calculator
- Geometric mean Calculator
- Harmonic mean Calculator
- Mean Calculator
- Root mean square Calculator
- Factor Calculator
- Modulo Calculator
- Prime number Calculator
- GCF Calculator
- LCM Calculator
- Prime factorization Calculator
- Absolute value Calculator
- Addition Calculator
- Binary subtraction Calculator
- GCF and LCM Calculator
- Long division Calculator
- Pascal's triangle Calculator
- Reciprocal Calculator
- Standard form Calculator
- Two's complement Calculator
- Weighted average Calculator
- e power x Calculator
Coordinate Geometry Calculators 📈
- Rise over run calculator Calculator
- Slope Calculator
- Perpendicular line Calculator
- Distance Calculator
- Angle between two vectors Calculator
- Dot product Calculator
- Cross product Calculator
- Average rate of change Calculator
- Cylindrical coordinates Calculator
- Equation of a circle Calculator
- Gradient Calculator
- Least squares regression line Calculator
- Linear interpolation Calculator
- Midpoint Calculator
- Parabola Calculator
- Parallel line Calculator
- Polar coordinates Calculator
- Slope intercept form Calculator
- Spherical coordinates Calculator
- Three-dimensional distance Calculator
Linear algebra calculators 🔢
- (Reduced) row echelon form Calculator
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- Diagonalize matrix Calculator
- Eigenvalue and eigenvector Calculator
- Gram-Schmidt Calculator
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- Linear independence Calculator
- Matrix addition and subtraction Calculator
- Matrix determinant Calculator
- Matrix multiplication Calculator
- Matrix rank Calculator
- Matrix transpose Calculator
- Systems of equations Calculator
- Unit vector Calculator
- Vector magnitude Calculator
- Vector projection Calculator
Other Math calculators
- Significant figures Calculator
- Scientific notation Calculator
- Golden ratio Calculator
