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- Maths Formulas
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- Long Addition Calculator
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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
- Characteristic polynomial Calculator
- Cramer's rule Calculator
- Diagonalize matrix Calculator
- Eigenvalue and eigenvector Calculator
- Gram-Schmidt Calculator
- Inverse matrix Calculator
- 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